Roboguru

Diketahui segitiga  dengan titik sudut masing-masing ,  dan . Tentukan: c. Gambar segitiga  dan bayangan segitiga  pada rotasi  searah jarum jam dengan pusat rotasi .

Pertanyaan

Diketahui segitiga ABC dengan titik sudut masing-masing straight A open parentheses 2 comma space 1 close parenthesesstraight B open parentheses 4 comma space 2 close parentheses dan straight C open parentheses 2 comma space 4 close parentheses. Tentukan:

c. Gambar segitiga ABC dan bayangan segitiga ABC pada rotasi 45 degree searah jarum jam dengan pusat rotasi straight P open parentheses negative 1 comma space minus 1 close parentheses.

Pembahasan Soal:

Rotasi terhadap titik asal straight P open parentheses h comma space k close parentheses, dengan sudut rotasi theta, dapat dihitung dengan rumus berikut.

open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses equals open parentheses table row cell cos space theta end cell cell negative sin space theta end cell row cell sin space theta end cell cell cos space theta end cell end table close parentheses open parentheses table row cell x minus h end cell row cell y minus k end cell end table close parentheses plus open parentheses table row h row k end table close parentheses

Diketahui segitiga ABC dengan titik sudut masing-masing straight A open parentheses 2 comma space 1 close parenthesesstraight B open parentheses 4 comma space 2 close parentheses dan straight C open parentheses 2 comma space 4 close parentheses.

Akan ditentukan gambar segitiga ABC dan bayangan segitiga ABC pada rotasi 45 degree searah jarum jam dengan pusat rotasi straight P open parentheses negative 1 comma space minus 1 close parentheses. Karena rotasi searah jarum jam, maka Rotasi bernilai negatif.

Menentukan bayangan titik straight A open parentheses 2 comma space 1 close parentheses.

begin mathsize 12px style straight A open parentheses 2 comma space 1 close parentheses rightwards arrow with open square brackets straight P open parentheses negative 1 comma space minus 1 close parentheses comma space straight R open parentheses negative 45 degree close parentheses close square brackets on top straight A apostrophe open parentheses x apostrophe comma space y apostrophe close parentheses table attributes columnalign right center left columnspacing 2px end attributes row cell open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell cos space open parentheses negative 45 degree close parentheses end cell cell negative sin space open parentheses negative 45 degree close parentheses end cell row cell sin space open parentheses negative 45 degree close parentheses end cell cell cos space open parentheses negative 45 degree close parentheses end cell end table close parentheses open parentheses table row cell 2 minus open parentheses negative 1 close parentheses end cell row cell 1 minus open parentheses negative 1 close parentheses end cell end table close parentheses plus open parentheses table row cell negative 1 end cell row cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell cos space 45 degree end cell cell sin space 45 degree end cell row cell negative sin space 45 degree end cell cell cos space 45 degree end cell end table close parentheses open parentheses table row cell 2 plus 1 end cell row cell 1 plus 1 end cell end table close parentheses plus open parentheses table row cell negative 1 end cell row cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 1 half square root of 2 end cell cell 1 half square root of 2 end cell row cell negative 1 half square root of 2 end cell cell 1 half square root of 2 end cell end table close parentheses open parentheses table row 3 row 2 end table close parentheses plus open parentheses table row cell negative 1 end cell row cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 3 over 2 square root of 2 plus 2 over 2 square root of 2 end cell row cell negative 3 over 2 square root of 2 plus 2 over 2 square root of 2 end cell end table close parentheses plus open parentheses table row cell negative 1 end cell row cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 5 over 2 square root of 2 end cell row cell negative 1 half square root of 2 end cell end table close parentheses plus open parentheses table row cell negative 1 end cell row cell negative 1 end cell end table close parentheses end cell row cell open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell 5 over 2 square root of 2 minus 1 end cell row cell negative 1 half square root of 2 minus 1 end cell end table close parentheses end cell end table straight A open parentheses 2 comma space 1 close parentheses rightwards arrow with open square brackets straight P open parentheses negative 1 comma space minus 1 close parentheses comma space straight R open parentheses negative 45 degree close parentheses close square brackets on top straight A apostrophe open parentheses 5 over 2 square root of 2 minus 1 comma space minus 1 half square root of 2 minus 1 close parentheses end style 

Menentukan bayangan titik straight B open parentheses 4 comma space 2 close parentheses.

begin mathsize 12px style straight B open parentheses 4 comma space 2 close parentheses rightwards arrow with open square brackets straight P open parentheses negative 1 comma space minus 1 close parentheses comma space straight R open parentheses negative 45 degree close parentheses close square brackets on top straight B apostrophe open parentheses x apostrophe comma space y apostrophe close parentheses table attributes columnalign right center left columnspacing 2px end attributes row cell open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell cos space open parentheses negative 45 degree close parentheses end cell cell negative sin space open parentheses negative 45 degree close parentheses end cell row cell sin space open parentheses negative 45 degree close parentheses end cell cell cos space open parentheses negative 45 degree close parentheses end cell end table close parentheses open parentheses table row cell 4 minus open parentheses negative 1 close parentheses end cell row cell 2 minus open parentheses negative 1 close parentheses end cell end table close parentheses plus open parentheses table row cell negative 1 end cell row cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell cos space 45 degree end cell cell sin space 45 degree end cell row cell negative sin space 45 degree end cell cell cos space 45 degree end cell end table close parentheses open parentheses table row cell 4 plus 1 end cell row cell 2 plus 1 end cell end table close parentheses plus open parentheses table row cell negative 1 end cell row cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 1 half square root of 2 end cell cell 1 half square root of 2 end cell row cell negative 1 half square root of 2 end cell cell 1 half square root of 2 end cell end table close parentheses open parentheses table row 5 row 3 end table close parentheses plus open parentheses table row cell negative 1 end cell row cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 5 over 2 square root of 2 plus 3 over 2 square root of 2 end cell row cell negative 5 over 2 square root of 2 plus 3 over 2 square root of 2 end cell end table close parentheses plus open parentheses table row cell negative 1 end cell row cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 8 over 2 square root of 2 end cell row cell negative 2 over 2 square root of 2 end cell end table close parentheses plus open parentheses table row cell negative 1 end cell row cell negative 1 end cell end table close parentheses end cell row cell open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell 4 square root of 2 minus 1 end cell row cell negative square root of 2 minus 1 end cell end table close parentheses end cell end table straight B open parentheses 4 comma space 2 close parentheses rightwards arrow with open square brackets straight P open parentheses negative 1 comma space minus 1 close parentheses comma space straight R open parentheses negative 45 degree close parentheses close square brackets on top straight B apostrophe open parentheses 4 square root of 2 minus 1 comma space minus square root of 2 minus 1 close parentheses end style

Menentukan bayangan titik straight C open parentheses 2 comma space 4 close parentheses.

begin mathsize 12px style straight C open parentheses 2 comma space 4 close parentheses rightwards arrow with open square brackets straight P open parentheses negative 1 comma space minus 1 close parentheses comma space straight R open parentheses negative 45 degree close parentheses close square brackets on top straight C apostrophe open parentheses x apostrophe comma space y apostrophe close parentheses table attributes columnalign right center left columnspacing 2px end attributes row cell open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell cos space open parentheses negative 45 degree close parentheses end cell cell negative sin space open parentheses negative 45 degree close parentheses end cell row cell sin space open parentheses negative 45 degree close parentheses end cell cell cos space open parentheses negative 45 degree close parentheses end cell end table close parentheses open parentheses table row cell 2 minus open parentheses negative 1 close parentheses end cell row cell 4 minus open parentheses negative 1 close parentheses end cell end table close parentheses plus open parentheses table row cell negative 1 end cell row cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell cos space 45 degree end cell cell sin space 45 degree end cell row cell negative sin space 45 degree end cell cell cos space 45 degree end cell end table close parentheses open parentheses table row cell 2 plus 1 end cell row cell 4 plus 1 end cell end table close parentheses plus open parentheses table row cell negative 1 end cell row cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 1 half square root of 2 end cell cell 1 half square root of 2 end cell row cell negative 1 half square root of 2 end cell cell 1 half square root of 2 end cell end table close parentheses open parentheses table row 3 row 5 end table close parentheses plus open parentheses table row cell negative 1 end cell row cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 3 over 2 square root of 2 plus 5 over 2 square root of 2 end cell row cell negative 3 over 2 square root of 2 plus 5 over 2 square root of 2 end cell end table close parentheses plus open parentheses table row cell negative 1 end cell row cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 8 over 2 square root of 2 end cell row cell 2 over 2 square root of 2 end cell end table close parentheses plus open parentheses table row cell negative 1 end cell row cell negative 1 end cell end table close parentheses end cell row cell open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell 4 square root of 2 minus 1 end cell row cell square root of 2 minus 1 end cell end table close parentheses end cell end table straight C open parentheses 2 comma space 4 close parentheses rightwards arrow with open square brackets straight P open parentheses negative 1 comma space minus 1 close parentheses comma space straight R open parentheses negative 45 degree close parentheses close square brackets on top straight C apostrophe open parentheses 4 square root of 2 minus 1 comma space square root of 2 minus 1 close parentheses end style

Jadi, diperoleh titik koordinat bayangan segitiga ABC adalah straight A apostrophe open parentheses 5 over 2 square root of 2 minus 1 comma space minus 1 half square root of 2 minus 1 close parenthesesstraight B apostrophe open parentheses 4 square root of 2 minus 1 comma space minus square root of 2 minus 1 close parentheses dan straight C apostrophe open parentheses 4 square root of 2 minus 1 comma space square root of 2 minus 1 close parentheses.

Jika digambarkan akan menjadi seperti berikut.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

Y. Fathoni

Mahasiswa/Alumni Universitas Negeri Yogyakarta.

Terakhir diupdate 01 Mei 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Akibat rotasi  dari titik  mempunyai bayangan . Koordinat titik  adalah .... (Kinomatika 2014)

Pembahasan Soal:

Diketahui,

  • straight P left parenthesis 1 comma space 2 right parenthesis
  • Dirotasikan oleh  begin mathsize 14px style open square brackets straight P open parentheses 1 comma space 2 close parentheses comma space straight R open parentheses 1 half straight pi close parentheses close square brackets end style
  •  Error converting from MathML to accessible text.

Ditanyakan,

  • Koordinat titik straight A

Gunakan persamaan matriks berikut.

open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses equals open parentheses table row cell cos space straight theta end cell cell negative sin space straight theta end cell row cell sin space straight theta end cell cell cos space straight theta end cell end table close parentheses open parentheses table row cell x minus h end cell row cell y minus k end cell end table close parentheses plus open parentheses table row h row k end table close parentheses

Maka,

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell cos space 90 end cell cell negative sin space 90 end cell row cell sin space 90 end cell cell cos space 90 end cell end table close parentheses open parentheses table row cell x minus 1 end cell row cell y minus 2 end cell end table close parentheses plus open parentheses table row 1 row 2 end table close parentheses end cell row cell open parentheses table row 3 row 7 end table close parentheses end cell equals cell open parentheses table row 0 cell negative 1 end cell row 1 0 end table close parentheses open parentheses table row cell x minus 1 end cell row cell y minus 2 end cell end table close parentheses plus open parentheses table row 1 row 2 end table close parentheses end cell row cell open parentheses table row 3 row 7 end table close parentheses end cell equals cell open parentheses table row cell negative 1 left parenthesis y minus 2 right parenthesis end cell row cell 1 left parenthesis x minus 1 right parenthesis end cell end table close parentheses plus open parentheses table row 1 row 2 end table close parentheses end cell row cell open parentheses table row 3 row 7 end table close parentheses end cell equals cell open parentheses table row cell negative y plus 2 end cell row cell x minus 1 end cell end table close parentheses plus open parentheses table row 1 row 2 end table close parentheses end cell row cell open parentheses table row 3 row 7 end table close parentheses end cell equals cell open parentheses table row cell negative y plus 2 plus 1 end cell row cell x minus 1 plus 2 end cell end table close parentheses end cell row cell open parentheses table row 3 row 7 end table close parentheses end cell equals cell open parentheses table row cell negative y plus 3 end cell row cell x plus 1 end cell end table close parentheses end cell row blank blank blank row 3 equals cell negative y plus 3 end cell row y equals cell 3 minus 3 end cell row y equals 0 row blank blank blank row 7 equals cell x plus 1 end cell row x equals cell 7 minus 1 end cell row x equals 6 row blank blank blank end table

Jadi, koordinat titik straight A adalah left parenthesis 6 comma 0 right parenthesis.

Oleh karena itu, jawaban yang benar adalah D.

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Roboguru

Jika garis  dirotasi sejauh  dengan titik pusat , maka petanya adalah ....

Pembahasan Soal:

Persamaan transformasi dengan pusat open parentheses a comma space b close parentheses dan sudut rotasi theta berlawanan arah jarum jam, untuk pemetaan left parenthesis x comma space y right parenthesis ke left parenthesis x apostrophe comma space y apostrophe right parenthesis dapat dinyatakan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell cos theta end cell cell negative sin theta end cell row cell sin theta end cell cell cos theta end cell end table close parentheses open parentheses table row cell x minus a end cell row cell y minus b end cell end table close parentheses plus open parentheses table row a row b end table close parentheses end cell end table  

Maka garis y equals 3 x dirotasi sejauh 90 degree dengan titik pusat straight A open parentheses 4 comma space 2 close parentheses, hasilnya adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell cos theta end cell cell negative sin theta end cell row cell sin theta end cell cell cos theta end cell end table close parentheses open parentheses table row cell x minus a end cell row cell y minus b end cell end table close parentheses plus open parentheses table row a row b end table close parentheses end cell row cell open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell cos 90 degree end cell cell negative sin 90 degree end cell row cell sin 90 degree end cell cell cos 90 degree end cell end table close parentheses open parentheses table row cell x minus 4 end cell row cell y minus 2 end cell end table close parentheses plus open parentheses table row 4 row 2 end table close parentheses end cell row cell open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row 0 cell negative 1 end cell row 1 0 end table close parentheses open parentheses table row cell x minus 4 end cell row cell y minus 2 end cell end table close parentheses plus open parentheses table row 4 row 2 end table close parentheses end cell row cell open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell 0 times open parentheses x minus 4 close parentheses plus open parentheses negative 1 close parentheses open parentheses y minus 2 close parentheses end cell row cell 1 times open parentheses x minus 4 close parentheses plus 0 times open parentheses y minus 2 close parentheses end cell end table close parentheses plus open parentheses table row 4 row 2 end table close parentheses end cell row cell open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell 2 minus y end cell row cell x minus 4 end cell end table close parentheses plus open parentheses table row 4 row 2 end table close parentheses end cell row cell open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell 6 minus y end cell row cell x minus 2 end cell end table close parentheses end cell row blank blank blank end table 

Berdasarkan kesamaan matriks di atas diperoleh:

x apostrophe equals 6 minus y space left right arrow space y equals 6 minus x apostrophe y apostrophe equals x minus 2 space left right arrow space x equals y apostrophe plus 2         

Substitusikan nilai x dan y yang diperoleh ke persamaan awal.

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell 3 x end cell row cell 6 minus x apostrophe end cell equals cell 3 open parentheses y apostrophe plus 2 close parentheses end cell row cell up diagonal strike 6 minus x apostrophe end cell equals cell 3 y apostrophe plus up diagonal strike 6 end cell row cell negative x apostrophe plus x apostrophe end cell equals cell 3 y apostrophe plus x apostrophe end cell row 0 equals cell x apostrophe plus 3 y apostrophe end cell end table 

Sehingga diperoleh petanya adalah x plus 3 y equals 0

Jadi, jawaban yang tepat adalah B.

0

Roboguru

Diberikan jajargenjang  dengan , , , dan . Tuliskan bayangan dari data berikut! b. Garis  dirotasi oleh .

Pembahasan Soal:

  • Menentukan garis l identical to garis space B C dengan  titik straight B left parenthesis 4 comma 4 right parenthesis dan straight C left parenthesis 2 comma 4 right parenthesis.

          Persamaan garis B C adalah 

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses y minus y subscript 1 close parentheses open parentheses x subscript 2 minus x subscript 1 close parentheses end cell equals cell open parentheses x minus x subscript 1 close parentheses open parentheses y subscript 2 minus y subscript 1 close parentheses end cell row cell open parentheses y minus 4 close parentheses open parentheses 2 minus 4 close parentheses end cell equals cell open parentheses x minus 4 close parentheses open parentheses 4 minus 4 close parentheses end cell row cell left parenthesis y minus 4 right parenthesis left parenthesis negative 2 right parenthesis end cell equals cell open parentheses x minus 4 close parentheses open parentheses 0 close parentheses end cell row cell negative 2 y plus 8 end cell equals 0 row cell negative 2 y end cell equals cell negative 8 end cell row y equals 4 end table

Jadi, garis B C identical to l equals y minus 4 equals 0.

  • Di rotasi oleh open square brackets straight A left parenthesis 2 comma 0 right parenthesis comma space straight R left parenthesis negative 60 degree close square brackets

Kita akan melakukan dengan cara eliminasi Gauss-Jordan dalam menjawab soal ini.

Persamaan matriks Gauss-Jordan:

open parentheses table row cell cos space open parentheses negative 60 degree close parentheses end cell cell negative sin space open parentheses negative 60 degree close parentheses end cell row cell sin space open parentheses negative 60 degree close parentheses end cell cell cos space open parentheses negative 60 degree close parentheses end cell end table vertical ellipsis table row cell x apostrophe minus 2 end cell row cell y apostrophe minus 0 end cell end table close parentheses equals open parentheses table row cell 1 half end cell cell fraction numerator square root of 3 over denominator 2 end fraction end cell row cell negative fraction numerator square root of 3 over denominator 2 end fraction end cell cell 1 half end cell end table vertical ellipsis table row cell x apostrophe minus 2 end cell row cell y apostrophe end cell end table close parentheses

Proses Eliminasi Gauss-Jordan:

open parentheses table row cell 1 half end cell cell fraction numerator square root of 3 over denominator 2 end fraction end cell row cell negative fraction numerator square root of 3 over denominator 2 end fraction end cell cell 1 half end cell end table vertical ellipsis table row cell x apostrophe minus 2 end cell row cell y apostrophe end cell end table close parentheses table row cell 2 B subscript 1 end cell row cell 2 B subscript 2 end cell end table left right double arrow open parentheses table row 1 cell square root of 3 end cell row cell negative square root of 3 end cell 1 end table vertical ellipsis table row cell 2 x apostrophe minus 4 end cell row cell 2 y apostrophe end cell end table close parentheses table row blank row cell square root of 3 B subscript 1 plus B subscript 2 end cell end table left right double arrow open parentheses table row 1 cell square root of 3 end cell row 0 4 end table vertical ellipsis table row cell 2 x apostrophe minus 4 end cell row cell 2 square root of 2 x apostrophe minus 4 square root of 3 plus 2 y apostrophe end cell end table close parentheses table row blank row cell 1 fourth end cell end table left right double arrow open parentheses table row 1 cell square root of 3 end cell row 0 1 end table vertical ellipsis table row cell 2 x apostrophe minus 4 end cell row cell 1 half square root of 2 x apostrophe minus square root of 3 plus 1 half y apostrophe end cell end table close parentheses table row cell negative square root of 3 B subscript 2 plus B subscript 1 end cell row blank end table left right double arrow open parentheses table row 1 0 row 0 1 end table vertical ellipsis table row cell open parentheses 2 minus fraction numerator square root of 6 over denominator 2 end fraction close parentheses x apostrophe minus fraction numerator square root of 3 over denominator 2 end fraction y apostrophe minus 1 end cell row cell 1 half square root of 2 x apostrophe minus square root of 3 plus 1 half y apostrophe end cell end table close parentheses

Hal ini berarti:

table attributes columnalign right center left columnspacing 0px end attributes row cell x minus 2 end cell equals cell open parentheses 2 minus fraction numerator square root of 6 over denominator 2 end fraction close parentheses x apostrophe minus fraction numerator square root of 3 over denominator 2 end fraction y apostrophe minus 1 end cell row x equals cell open parentheses 2 minus fraction numerator square root of 6 over denominator 2 end fraction close parentheses x apostrophe minus fraction numerator square root of 3 over denominator 2 end fraction y apostrophe plus 1 space... left parenthesis 1 right parenthesis end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell y minus 0 end cell equals cell 1 half square root of 2 x apostrophe minus square root of 3 plus 1 half y apostrophe end cell row y equals cell 1 half square root of 2 x apostrophe minus square root of 3 plus 1 half y apostrophe space... left parenthesis 2 right parenthesis end cell end table

Kedua persamaan di atas disubstitusikan ke persamaan garis y minus 4 equals 0:

table attributes columnalign right center left columnspacing 0px end attributes row cell y minus 4 end cell equals 0 row cell 1 half square root of 2 x apostrophe minus square root of 3 plus 1 half y apostrophe minus 4 end cell equals 0 row cell square root of 2 x apostrophe plus y apostrophe minus 2 square root of 3 minus 8 end cell equals 0 end table

Jadi, persamaan bayangan garis l identical to B C adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 2 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank y end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 8 end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 0 end table.

 

 

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Roboguru

Titik sudut suatu segitiga adalah , , dan . Carilah bayangan titik sudut segitiga itu karena putaran dengan pusat  dan sudut putar , serta pusat  dan sudut putar . b. Tentukan bayangan dari , , , , ,...

Pembahasan Soal:

  • Menentukan bayangan titik dengan matriks transformasi pada bagian soal nomor a:

begin mathsize 12px style open parentheses table row cell x subscript A apostrophe end cell row cell y subscript A apostrophe end cell end table table row cell x subscript B apostrophe end cell row cell y subscript B apostrophe end cell end table table row cell x subscript C apostrophe end cell row cell y subscript C apostrophe end cell end table table row cell x subscript D apostrophe end cell row cell y subscript D apostrophe end cell end table table row cell x subscript E apostrophe end cell row cell y subscript E apostrophe end cell end table table row cell x subscript F apostrophe end cell row cell y subscript F apostrophe end cell end table close parentheses equals open parentheses table row cell cos space alpha space end cell cell negative sin space alpha end cell row cell sin space alpha end cell cell cos space alpha end cell end table close parentheses open parentheses table row cell x subscript A end cell row cell y subscript A end cell end table table row cell x subscript B end cell row cell y subscript B end cell end table table row cell x subscript C end cell row cell y subscript C end cell end table table row cell x subscript D end cell row cell y subscript D end cell end table table row cell x subscript E end cell row cell y subscript E end cell end table table row cell x subscript F end cell row cell y subscript F end cell end table close parentheses open parentheses table row cell x subscript A apostrophe end cell row cell y subscript A apostrophe end cell end table table row cell x subscript B apostrophe end cell row cell y subscript B apostrophe end cell end table table row cell x subscript C apostrophe end cell row cell y subscript C apostrophe end cell end table table row cell x subscript D apostrophe end cell row cell y subscript D apostrophe end cell end table table row cell x subscript E apostrophe end cell row cell y subscript E apostrophe end cell end table table row cell x subscript F apostrophe end cell row cell y subscript F apostrophe end cell end table close parentheses equals open parentheses table row cell cos space 1 third straight pi space end cell cell negative sin space 1 third straight pi end cell row cell sin space 1 third straight pi end cell cell cos space 1 third straight pi end cell end table close parentheses open parentheses table row 0 cell square root of 3 end cell cell square root of 3 end cell cell negative 2 end cell cell negative square root of 3 end cell 1 row 2 1 cell negative 1 end cell 0 cell negative 1 end cell cell negative square root of 3 end cell end table close parentheses open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses equals open parentheses table row cell 1 half end cell cell negative 1 half square root of 3 end cell row cell 1 half square root of 3 end cell cell 1 half end cell end table close parentheses open parentheses table row 0 cell square root of 3 end cell cell square root of 3 end cell cell negative 2 end cell cell negative square root of 3 end cell 1 row 2 1 cell negative 1 end cell 0 cell negative 1 end cell cell negative square root of 3 end cell end table close parentheses open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses equals open parentheses table row cell negative square root of 3 end cell 0 cell square root of 3 end cell cell negative 1 end cell 0 2 row 1 2 1 cell negative square root of 3 end cell cell negative 2 end cell 0 end table close parentheses end style

Jadi, bayangan dari titik-titik tersebut adalah 

A apostrophe open parentheses negative square root of 3 comma space 1 close parentheses comma space B apostrophe open parentheses 0 comma space 2 close parentheses comma space C apostrophe open parentheses square root of 3 comma space 1 close parentheses comma space D apostrophe open parentheses negative 1 comma space minus square root of 3 close parentheses comma space E apostrophe open parentheses 0 comma space minus 2 close parentheses comma space F open parentheses 2 comma space 0 close parentheses

0

Roboguru

Salinlah gambar berikut pada kertas berpetak. Gambarkan bangun hasil  sesuai data di bawah ini. a.

Pembahasan Soal:

begin mathsize 14px style open square brackets straight P comma space straight R open parentheses straight pi over 3 close parentheses close square brackets end style artinya triangle ABC di rotasikan :

 table attributes columnalign right center left columnspacing 0px end attributes row cell straight pi over 3 end cell equals cell 180 over 3 end cell row blank equals 60 end table


 

Jadi, gambar bangun hasil begin mathsize 14px style triangle ABC end style dengan  begin mathsize 14px style open square brackets straight P comma space straight R open parentheses straight pi over 3 close parentheses close square brackets end style seperti di atas.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

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