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Tentukan bayangan dari segitiga ABC dengan A(2,1), B(6,1) dan C(2,5) jika diputar 90∘ dengan pusat (0,0) lalu dicerminkan terhadap sumbu x, kemudian digeser (−2−3​)!

Pertanyaan

Tentukan bayangan dari segitiga ABC dengan straight A open parentheses 2 comma 1 close parentheses comma straight B open parentheses 6 comma 1 close parentheses dan straight C open parentheses 2 comma 5 close parentheses jika diputar 90 degree dengan pusat open parentheses 0 comma 0 close parentheses lalu dicerminkan terhadap sumbu x comma kemudian digeser open parentheses table row cell negative 2 end cell row cell negative 3 end cell end table close parentheses factorial 

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

bayangan dari segitiga ABC pada soal tersebut adalah straight A apostrophe apostrophe apostrophe open parentheses negative 3 comma negative 5 close parentheses comma table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight B apostrophe apostrophe apostrophe open parentheses negative 3 comma negative 9 close parentheses end cell end table dan table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight C apostrophe apostrophe apostrophe open parentheses negative 7 comma negative 5 close parentheses. end cell end table 

Pembahasan

Ingat kembali rumus berikut:

  • Rotasi 90 degree dengan pusat open parentheses 0 comma 0 close parentheses

straight A open parentheses x italic comma y close parentheses space rightwards arrow with open square brackets straight O comma 90 degree close square brackets on top space straight A apostrophe open parentheses x italic apostrophe equals italic minus y italic comma y apostrophe equals x close parentheses

  • Refleksi terhadap sumbunegative x

straight A open parentheses x italic comma y close parentheses space rightwards arrow with s b space x on top space straight A apostrophe open parentheses x italic apostrophe equals x italic comma y apostrophe equals negative y close parentheses

  • Translasi pada titik

straight A open parentheses x italic comma y close parentheses space rightwards arrow with straight T open parentheses a comma b close parentheses on top space straight A apostrophe open parentheses x italic apostrophe equals x plus a italic comma y apostrophe equals y plus b close parentheses

Dengan menggunakan rumus di atas, maka bayangan dari segitiga ABC jika di rotasi 90 degree dengan pusat open parentheses 0 comma 0 close parentheses adalah 

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight A open parentheses x italic comma y close parentheses space rightwards arrow with open square brackets straight O comma 90 degree close square brackets on top space straight A apostrophe open parentheses x italic apostrophe equals italic minus y italic comma y apostrophe equals x close parentheses end cell row blank blank cell straight A open parentheses 2 comma 1 close parentheses space rightwards arrow with open square brackets straight O comma 90 degree close square brackets on top space straight A apostrophe open parentheses negative 1 comma 2 close parentheses end cell row blank blank cell straight B open parentheses 6 comma 1 close parentheses space rightwards arrow with open square brackets straight O comma 90 degree close square brackets on top space straight B apostrophe open parentheses negative 1 comma 6 close parentheses end cell row blank blank cell straight C open parentheses 2 comma 5 close parentheses space rightwards arrow with open square brackets straight O comma 90 degree close square brackets on top space straight C apostrophe open parentheses negative 5 comma 2 close parentheses end cell end table

Kemudian, akan dicerminkan terhadap sumbunegative x sebagai berikut:

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight A open parentheses x italic comma y close parentheses space rightwards arrow with s b space x on top space straight A apostrophe open parentheses x italic apostrophe equals x italic comma y apostrophe equals negative y close parentheses end cell row blank blank cell straight A apostrophe open parentheses negative 1 comma 2 close parentheses space rightwards arrow with s b space x on top space straight A apostrophe apostrophe open parentheses negative 1 comma negative 2 close parentheses end cell row blank blank cell straight B apostrophe open parentheses negative 1 comma 6 close parentheses space rightwards arrow with s b space x on top space straight B apostrophe apostrophe open parentheses negative 1 comma negative 6 close parentheses end cell row blank blank cell straight C apostrophe open parentheses negative 5 comma 2 close parentheses space rightwards arrow with s b space x on top space straight C apostrophe apostrophe open parentheses negative 5 comma negative 2 close parentheses end cell end table

Selanjutnya, akan digeser/ditranslasi open parentheses table row cell negative 2 end cell row cell negative 3 end cell end table close parentheses sebagai berikut:

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight A open parentheses x italic comma y close parentheses space rightwards arrow with straight T open parentheses a comma b close parentheses on top space straight A apostrophe open parentheses x italic apostrophe equals x plus a italic comma y apostrophe equals y plus b close parentheses end cell row blank blank cell straight A double apostrophe open parentheses negative 1 comma negative 2 close parentheses space rightwards arrow with straight T open parentheses negative 2 comma negative 3 close parentheses on top space straight A apostrophe apostrophe apostrophe open parentheses negative 1 plus open parentheses negative 2 close parentheses comma negative 2 plus open parentheses negative 3 close parentheses close parentheses end cell row blank blank cell space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space straight A apostrophe apostrophe apostrophe open parentheses negative 3 comma negative 5 close parentheses end cell row blank blank cell straight B double apostrophe open parentheses negative 1 comma negative 6 close parentheses space rightwards arrow with straight T open parentheses negative 2 comma negative 3 close parentheses on top space straight B apostrophe apostrophe apostrophe open parentheses negative 1 plus open parentheses negative 2 close parentheses comma negative 6 plus open parentheses negative 3 close parentheses close parentheses end cell row blank blank cell space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space straight B apostrophe apostrophe apostrophe open parentheses negative 3 comma negative 9 close parentheses end cell row blank blank cell straight C double apostrophe open parentheses negative 5 comma negative 2 close parentheses space rightwards arrow with straight T open parentheses negative 2 comma negative 3 close parentheses on top space straight C apostrophe apostrophe apostrophe open parentheses negative 5 plus open parentheses negative 2 close parentheses comma negative 2 plus open parentheses negative 3 close parentheses close parentheses end cell row blank blank cell space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space straight C apostrophe apostrophe apostrophe open parentheses negative 7 comma negative 5 close parentheses end cell end table

Dengan demikian, bayangan dari segitiga ABC pada soal tersebut adalah straight A apostrophe apostrophe apostrophe open parentheses negative 3 comma negative 5 close parentheses comma table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight B apostrophe apostrophe apostrophe open parentheses negative 3 comma negative 9 close parentheses end cell end table dan table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight C apostrophe apostrophe apostrophe open parentheses negative 7 comma negative 5 close parentheses. end cell end table 

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Diketahui titik A(−3,7) ditranslasikan oleh T=(4−2​). Kemudian dicerminkan oleh x=−1. Selanjutnya garis dirotasi pada Pusat (0,0) dengan Sudut 90∘. Tentukan bayangan terakhir titik A !

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