Roboguru

Lukiskan sketsa △OAB dan bayangan △OAB pada kertas berpetak, kemudian tuliskan koordinat titik bayangannya, jika titik-titik sudut  adalah O(0,0), A(3,0), dan B(1,6) dirotasi oleh: c. [B(1,6),R(−180∘)]

Pertanyaan

Lukiskan sketsa begin mathsize 14px style triangle OAB end style dan bayangan begin mathsize 14px style triangle OAB end style pada kertas berpetak, kemudian tuliskan koordinat titik bayangannya, jika titik-titik sudut undefined adalah begin mathsize 14px style O left parenthesis 0 comma 0 right parenthesis end stylebegin mathsize 14px style A left parenthesis 3 comma 0 right parenthesis end style, dan begin mathsize 14px style B left parenthesis 1 comma 6 right parenthesis end style dirotasi oleh:

c. begin mathsize 14px style open square brackets straight B left parenthesis 1 comma 6 right parenthesis comma space straight R left parenthesis negative 180 degree right parenthesis close square brackets end style 

Pembahasan Soal:

1.  begin mathsize 14px style O left parenthesis 0 comma 0 right parenthesis end style

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 open parentheses negative 180 close parentheses space end cell cell negative sin space open parentheses negative 180 close parentheses space end cell row cell sin space open parentheses negative 180 close parentheses space end cell cell cos space open parentheses negative 180 close parentheses space 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 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 space 180 space end cell cell sin space 180 end cell row cell negative sin space 180 end cell cell cos space 180 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 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 negative 1 end cell 0 row 0 cell negative 1 end cell end table close parentheses open parentheses table row cell 0 minus 1 end cell row cell 0 minus 6 end cell end table close parentheses plus open parentheses table row 1 row 6 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 end cell 0 row 0 cell negative 1 end cell end table close parentheses open parentheses table row cell negative 1 end cell row cell negative 6 end cell end table close parentheses plus open parentheses table row 1 row 6 end table close parentheses end cell row blank equals cell open parentheses table row 1 row 6 end table close parentheses plus open parentheses table row 1 row 6 end table close parentheses end cell row blank equals cell open parentheses table row 2 row 12 end table close parentheses end cell row blank blank blank end table

2. straight A left parenthesis 3 comma 0 right parenthesis

 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 open parentheses negative 180 close parentheses space end cell cell negative sin space open parentheses negative 180 close parentheses space end cell row cell sin space open parentheses negative 180 close parentheses space end cell cell cos space open parentheses negative 180 close parentheses space 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 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 space 180 space end cell cell sin space 180 end cell row cell negative sin space 180 end cell cell cos space 180 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 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 negative 1 end cell 0 row 0 cell negative 1 end cell end table close parentheses open parentheses table row cell 3 minus 1 end cell row cell 0 minus 6 end cell end table close parentheses plus open parentheses table row 1 row 6 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 end cell 0 row 0 cell negative 1 end cell end table close parentheses open parentheses table row 2 row cell negative 6 end cell end table close parentheses plus open parentheses table row 1 row 6 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 2 end cell row 6 end table close parentheses plus open parentheses table row 1 row 6 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 end cell row 12 end table close parentheses end cell row blank blank blank end table

3. straight B left parenthesis 1 comma 6 right parenthesis

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 open parentheses negative 180 close parentheses space end cell cell negative sin space open parentheses negative 180 close parentheses space end cell row cell sin space open parentheses negative 180 close parentheses space end cell cell cos space open parentheses negative 180 close parentheses space 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 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 space 180 space end cell cell sin space 180 end cell row cell negative sin space 180 end cell cell cos space 180 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 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 negative 1 end cell 0 row 0 cell negative 1 end cell end table close parentheses open parentheses table row cell 1 minus 1 end cell row cell 6 minus 6 end cell end table close parentheses plus open parentheses table row 1 row 6 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 end cell 0 row 0 cell negative 1 end cell end table close parentheses open parentheses table row 0 row 0 end table close parentheses plus open parentheses table row 1 row 6 end table close parentheses end cell row blank equals cell open parentheses table row 0 row 0 end table close parentheses plus open parentheses table row 1 row 6 end table close parentheses end cell row blank equals cell open parentheses table row 1 row 6 end table close parentheses end cell row blank blank blank end table

Di dapatkan titik-titik sudut bayangan straight O apostrophe left parenthesis 2 comma 12 right parenthesisstraight A apostrophe left parenthesis negative 1 comma 12 right parenthesis dan straight B apostrophe left parenthesis 1 comma 6 right parenthesis.

Sketsa begin mathsize 14px style triangle OAB end style dan bayangan begin mathsize 14px style triangle OAB end style


Jadi, sketsa begin mathsize 14px style triangle OAB end style dan bayangan begin mathsize 14px style triangle OAB end style di gambarkan seperti di atas.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

G. Albiah

Mahasiswa/Alumni Universitas Galuh Ciamis

Terakhir diupdate 06 Oktober 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Garis x + y = 5 dirotasi sebesar 45° berlawanan arah jarum jam dengan pusat P(1,-3). Bayangan dari garis tersebut adalah ....

Pembahasan Soal:

Misalkan titik A(x, y) terletak pada garis tersebut.
Kemudian titik tersebut juga dirotasikan terhadap pusat (1,-3). Sehingga a = 1 dan b = -3.
Besar sudut rotasinya adalah 45° berlawanan arah jarum jam. Sehingga θ = 45°.
Misalkan bayangannya adalah A’(x’,y’), maka didapatkan hubungan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses table row cell x to the power of apostrophe end cell row cell y to the power of apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell cos invisible function application theta end cell cell negative sin invisible function application theta end cell row cell sin invisible function application theta end cell cell cos invisible function application 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 to the power of apostrophe end cell row cell y to the power of apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell cos invisible function application 45 degree end cell cell negative sin invisible function application 45 degree end cell row cell sin invisible function application 45 degree end cell cell cos invisible function application 45 degree end cell end table close parentheses open parentheses table row cell x minus 1 end cell row cell y minus open parentheses negative 3 close parentheses end cell end table close parentheses plus open parentheses table row 1 row cell negative 3 end cell end table close parentheses end cell row cell open parentheses table row cell x to the power of apostrophe end cell row cell y to the power of apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell 1 half square root of 2 end cell cell negative 1 half square root of 2 end cell row cell 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 cell x minus 1 end cell row cell y plus 3 end cell end table close parentheses plus open parentheses table row 1 row cell negative 3 end cell end table close parentheses end cell row cell open parentheses table row cell x to the power of apostrophe end cell row cell y to the power of apostrophe end cell end table close parentheses minus open parentheses table row 1 row cell negative 3 end cell end table close parentheses end cell equals cell open parentheses table row cell 1 half square root of 2 end cell cell negative 1 half square root of 2 end cell row cell 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 cell x minus 1 end cell row cell y plus 3 end cell end table close parentheses end cell row cell open parentheses table row cell x to the power of apostrophe minus 1 end cell row cell y to the power of apostrophe plus 3 end cell end table close parentheses end cell equals cell open parentheses table row cell 1 half square root of 2 end cell cell negative 1 half square root of 2 end cell row cell 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 cell x minus 1 end cell row cell y plus 3 end cell end table close parentheses end cell row cell open parentheses table row cell 1 half square root of 2 end cell cell negative 1 half square root of 2 end cell row cell 1 half square root of 2 end cell cell 1 half square root of 2 end cell end table close parentheses to the power of negative 1 end exponent open parentheses table row cell x to the power of apostrophe minus 1 end cell row cell y to the power of apostrophe plus 3 end cell end table close parentheses end cell equals cell open parentheses table row cell x minus 1 end cell row cell y plus 3 end cell end table close parentheses end cell row cell fraction numerator 1 over denominator 1 half square root of 2 times 1 half square root of 2 minus open parentheses negative 1 half square root of 2 close parentheses times 1 half square root of 2 end fraction 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 cell x to the power of apostrophe minus 1 end cell row cell y to the power of apostrophe plus 3 end cell end table close parentheses end cell equals cell open parentheses table row cell x minus 1 end cell row cell y plus 3 end cell end table close parentheses end cell row cell fraction numerator 1 over denominator 1 half plus 1 half end fraction 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 cell x to the power of apostrophe minus 1 end cell row cell y to the power of apostrophe plus 3 end cell end table close parentheses end cell equals cell open parentheses table row cell x minus 1 end cell row cell y plus 3 end cell end table close parentheses end cell row cell 1 over 1 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 cell x to the power of apostrophe minus 1 end cell row cell y to the power of apostrophe plus 3 end cell end table close parentheses end cell equals cell open parentheses table row cell x minus 1 end cell row cell y plus 3 end cell end table close parentheses end cell row cell open parentheses table row cell 1 half square root of 2 open parentheses x to the power of apostrophe minus 1 close parentheses plus 1 half square root of 2 open parentheses y to the power of apostrophe plus 3 close parentheses end cell row cell negative 1 half square root of 2 open parentheses x to the power of apostrophe minus 1 close parentheses plus 1 half square root of 2 open parentheses y to the power of apostrophe plus 3 close parentheses end cell end table close parentheses end cell equals cell open parentheses table row cell x minus 1 end cell row cell y plus 3 end cell end table close parentheses end cell row cell open parentheses table row cell 1 half x to the power of apostrophe square root of 2 minus 1 half square root of 2 plus 1 half y to the power of apostrophe square root of 2 plus 3 over 2 square root of 2 end cell row cell negative 1 half x to the power of apostrophe square root of 2 plus 1 half square root of 2 plus 1 half y to the power of apostrophe square root of 2 plus 3 over 2 square root of 2 end cell end table close parentheses end cell equals cell open parentheses table row cell x minus 1 end cell row cell y plus 3 end cell end table close parentheses end cell row cell open parentheses table row cell 1 half x to the power of apostrophe square root of 2 plus 1 half y to the power of apostrophe square root of 2 plus square root of 2 end cell row cell negative 1 half x to the power of apostrophe square root of 2 plus 1 half y to the power of apostrophe square root of 2 plus 2 square root of 2 end cell end table close parentheses end cell equals cell open parentheses table row cell x minus 1 end cell row cell y plus 3 end cell end table close parentheses end cell end table end style

Sehingga didapat

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 1 half x to the power of apostrophe square root of 2 plus 1 half y to the power of apostrophe square root of 2 plus square root of 2 end cell equals cell x minus 1 end cell row x equals cell 1 half x to the power of apostrophe square root of 2 plus 1 half y to the power of apostrophe square root of 2 plus square root of 2 plus 1 end cell end table end style

dan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell negative 1 half x to the power of apostrophe square root of 2 plus 1 half y to the power of apostrophe square root of 2 plus 2 square root of 2 end cell equals cell y plus 3 end cell row y equals cell negative 1 half x to the power of apostrophe square root of 2 plus 1 half y to the power of apostrophe square root of 2 plus 2 square root of 2 minus 3 end cell end table end style

Titik A’(x’,y’) merupakan bayangan dari titik A(x,y). Karena titik A(x,y) terletak pada garis x + y = 5, maka titik A’(x’,y’) terletak pada bayangannya. Sehingga bentuklah parabola tersebut ke dalam bentuk x’ dan y’, menggunakan hubungan yang telah didapat sebelumnya, yaitu begin mathsize 14px style x equals 1 half x to the power of apostrophe square root of 2 plus 1 half y to the power of apostrophe square root of 2 plus square root of 2 plus 1 space d a n space y equals negative 1 half x to the power of apostrophe square root of 2 plus 1 half y to the power of apostrophe square root of 2 plus 2 square root of 2 minus 3 end style.

Maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x plus y end cell equals 5 row cell open parentheses 1 half x to the power of apostrophe square root of 2 plus 1 half y to the power of apostrophe square root of 2 plus square root of 2 plus 1 close parentheses plus open parentheses negative 1 half x to the power of apostrophe square root of 2 plus 1 half y to the power of apostrophe square root of 2 plus 2 square root of 2 minus 3 close parentheses end cell equals 5 row cell y to the power of apostrophe square root of 2 plus 3 square root of 2 minus 2 end cell equals 5 row cell y to the power of apostrophe square root of 2 end cell equals cell 5 minus 3 square root of 2 plus 2 end cell row cell y to the power of apostrophe square root of 2 end cell equals cell 7 minus 3 square root of 2 end cell row cell y to the power of apostrophe end cell equals cell fraction numerator 7 minus 3 square root of 2 over denominator square root of 2 end fraction end cell row cell y to the power of apostrophe end cell equals cell fraction numerator 7 minus 3 square root of 2 over denominator square root of 2 end fraction times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell row cell y to the power of apostrophe end cell equals cell fraction numerator 7 square root of 2 minus 6 over denominator 2 end fraction end cell end table end style

Dalam bentuk umum didapat garis bayangannya adalah begin mathsize 14px style y equals fraction numerator 7 square root of 2 minus 6 over denominator 2 end fraction end style.

0

Roboguru

Titik-titik sudut segitiga ABC adalah A(0,2), B(−3​,−1), dan C(3​,−1). Tentukan bayangan △ABC karena rotasi berikut. b. [P(2,1),R(−2π​)]

Pembahasan Soal:

Transformasi rotasi straight R open parentheses negative straight pi over 2 close parentheses.,

table attributes columnalign right center left columnspacing 0px end attributes row cell negative straight pi over 2 end cell equals cell negative 180 over 2 end cell row blank equals cell negative 90 end cell end table

Maka,

1. undefined

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 open parentheses negative 90 close parentheses end cell cell negative sin space open parentheses negative 90 close parentheses end cell row cell sin space open parentheses negative 90 close parentheses end cell cell cos space open parentheses negative 90 close parentheses 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 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 space 90 end cell cell sin space 90 end cell row cell negative sin space 90 end cell cell cos space 90 end cell end table close parentheses open parentheses table row cell 0 minus 2 end cell row cell 2 minus 1 end cell end table close parentheses plus open parentheses table row 2 row 1 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 1 row cell negative 1 end cell 0 end table close parentheses open parentheses table row cell negative 2 end cell row 1 end table close parentheses plus open parentheses table row 2 row 1 end table close parentheses end cell row blank equals cell open parentheses table row 1 row 2 end table close parentheses plus open parentheses table row 2 row 1 end table close parentheses end cell row blank equals cell open parentheses table row 3 row 3 end table close parentheses end cell end table

2. begin mathsize 14px style straight B left parenthesis negative square root of 3 comma space minus 1 right parenthesis end style

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 open parentheses negative 90 close parentheses end cell cell negative sin space open parentheses negative 90 close parentheses end cell row cell sin space open parentheses negative 90 close parentheses end cell cell cos space open parentheses negative 90 close parentheses 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 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 space 90 end cell cell sin space 90 end cell row cell negative sin space 90 end cell cell cos space 90 end cell end table close parentheses open parentheses table row cell 0 minus left parenthesis negative square root of 3 right parenthesis end root end cell row cell 2 minus left parenthesis negative 1 right parenthesis end cell end table close parentheses plus open parentheses table row cell negative square root of 3 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 0 1 row cell negative 1 end cell 0 end table close parentheses open parentheses table row cell square root of 3 end cell row 3 end table close parentheses plus open parentheses table row cell negative square root of 3 end cell row cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row 3 row cell negative square root of 3 end cell end table close parentheses plus open parentheses table row 2 row 1 end table close parentheses end cell row blank equals cell open parentheses table row 5 row cell 1 minus square root of 3 end cell end table close parentheses end cell end table

3. undefined

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 open parentheses negative 90 close parentheses end cell cell negative sin space open parentheses negative 90 close parentheses end cell row cell sin space open parentheses negative 90 close parentheses end cell cell cos space open parentheses negative 90 close parentheses 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 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 space 90 end cell cell sin space 90 end cell row cell negative sin space 90 end cell cell cos space 90 end cell end table close parentheses open parentheses table row cell 0 minus square root of 3 end cell row cell 2 minus left parenthesis negative 1 right parenthesis end cell end table close parentheses plus open parentheses table row cell square root of 3 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 0 1 row cell negative 1 end cell 0 end table close parentheses open parentheses table row cell negative square root of 3 end cell row 3 end table close parentheses plus open parentheses table row cell negative square root of 3 end cell row cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 3 end cell row cell square root of 3 end cell end table close parentheses plus open parentheses table row 2 row 1 end table close parentheses end cell row blank equals cell open parentheses table row 1 row cell 1 plus square root of 3 end cell end table close parentheses end cell end table

Jadi, titik-titik sudut segitiga begin mathsize 14px style ABC end style adalah straight A apostrophe left parenthesis 3 comma space 3 right parenthesis, straight B apostrophe left parenthesis 5 comma space 1 minus square root of 3 right parenthesis, dan straight C apostrophe left parenthesis 5 comma space 1 plus square root of 3 right parenthesis.

0

Roboguru

Garis g:3x−2y+12=0 dirotasikan sebesar 180° terhadap titik pusat ( 1 , 2). Hasil rotasi garis g mempunyai persamaan ..

Pembahasan Soal:

begin mathsize 14px style open parentheses table row cell x to the power of apostrophe end cell row cell y to the power of apostrophe end cell end table close parentheses equals open parentheses table row cell negative 1 end cell 0 row 0 cell negative 1 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 equals open parentheses table row cell negative x plus 2 end cell row cell negative y plus 4 end cell end table close parentheses end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x apostrophe end cell equals cell negative x plus 2 end cell row x equals cell negative x apostrophe plus 2 end cell end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell y to the power of apostrophe end cell equals cell negative y plus 4 end cell row y equals cell negative y to the power of apostrophe plus 4 end cell end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 3 x minus 2 y plus 12 end cell equals 0 row cell 3 left parenthesis negative x apostrophe plus 2 right parenthesis minus 2 left parenthesis negative y to the power of apostrophe plus 4 right parenthesis plus 12 end cell equals 0 row cell negative 3 x to the power of apostrophe plus 2 y to the power of apostrophe plus 10 end cell equals 0 row cell 3 x minus 2 y minus 10 end cell equals 0 end table end style

Jadi, hasil rotasi garis g adalah A. begin mathsize 14px style bold 3 bold italic x bold minus bold 2 bold italic y bold minus bold 10 bold equals bold 0 end style

1

Roboguru

Jika garis y=3x dirotasi sejauh 90∘ dengan pusat A(4,2), maka hasilnya adalah...

Pembahasan Soal:

Ingat bayangan rotasi dengan pusat left parenthesis a comma space b right parenthesis adalah

open parentheses table row cell x apostrophe minus a end cell row cell y apostrophe minus b 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 a end cell row cell y minus b end cell end table close parentheses

Diketahui pusat rotasi A left parenthesis 4 comma space 2 right parenthesis dan  theta equals 90 degree. Maka,

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

substitusi ke persamaan benda,

benda space colon space y equals 3 x bayangan space colon space minus x apostrophe plus 6 equals 3 left parenthesis y apostrophe plus 2 right parenthesis space space space space space space space space space space space space space space space space space space space space space space x plus 3 y equals 0

Jadi, jawaban yang tepat adalah C.

0

Roboguru

Titik (2a, -a) diputar 90 berlawanan arah jarum jam dengan pusat perputaran titik (1, 1). Jika hasil rotasi adalah (2 + a, -2), maka a = ...

Pembahasan Soal:

Ingat!

Rotasi dengan pusat (a, b) berlawanan arah, yaitu:

begin mathsize 12px style 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 alpha 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 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 style

 

Diketahui:

Titik (2a, a) diputar 90undefined berlawanan arah jarum jam dengan pusat perputaran di titik (1, 1) menghasilkan titik (2 + a, -2), maka:

begin mathsize 12px style open parentheses table row cell 2 plus a end cell row cell negative 2 end cell end table close parentheses equals open parentheses table row cell cos space 90 degree end cell cell negative sin space 90 degree end cell row cell sin space 90 degree end cell cell cos space 90 degree end cell end table close parentheses open parentheses table row cell 2 a minus 1 end cell row cell negative a minus 1 end cell end table close parentheses plus open parentheses table row 1 row 1 end table close parentheses  open parentheses table row cell 2 plus a end cell row cell negative 2 end cell end table close parentheses equals open parentheses table row 0 cell negative 1 end cell row 1 0 end table close parentheses open parentheses table row cell 2 a minus 1 end cell row cell negative a minus 1 end cell end table close parentheses plus open parentheses table row 1 row 1 end table close parentheses  open parentheses table row cell 2 plus a end cell row cell negative 2 end cell end table close parentheses equals open parentheses table row cell a plus 1 end cell row cell 2 a minus 1 end cell end table close parentheses plus open parentheses table row 1 row 1 end table close parentheses  open parentheses table row cell 2 plus a end cell row cell negative 2 end cell end table close parentheses equals open parentheses table row cell a plus 2 end cell row cell 2 a end cell end table close parentheses end style

Diperoleh:

- 2 = 2a

a = - 1

 

Jadi, nilai a adalah - 1.

1

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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