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Pertanyaan

Garis begin mathsize 14px style g colon 2 x plus y minus 2 equals 0 end style ditranslasikan oleh begin mathsize 14px style T equals open square brackets table row 4 row cell negative 2 end cell end table close square brackets end style, lalu dirotasikan sebear size 14px 90 size 14px degree terhadap titik pusat begin mathsize 14px style P left parenthesis 1 comma 2 right parenthesis end style. Tentukan hasil transformasi garis begin mathsize 14px style g end style.

I. Kumaralalita

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

persamaan garis hasil transformasinya adalah begin mathsize 14px style x minus 2 y plus 7 equals 0 end style 

Pembahasan

Misalkan titik begin mathsize 14px style open parentheses x comma space y close parentheses end style terletak pada garis begin mathsize 14px style g end style 

i) Hasil translasi titik undefined 

begin mathsize 14px style open square brackets table row cell x apostrophe end cell row cell y apostrophe end cell end table close square brackets equals open square brackets table row cell x plus a end cell row cell y plus b end cell end table close square brackets equals open square brackets table row cell x plus 4 end cell row cell y minus 2 end cell end table close square brackets end style 

ii) Rotasi titik begin mathsize 14px style open parentheses x apostrophe comma space y apostrophe close parentheses end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open square brackets table row cell x " end cell row cell y " end cell end table close square brackets end cell equals cell open square brackets 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 square brackets open square brackets table row cell x apostrophe minus 1 end cell row cell y apostrophe minus 2 end cell end table close square brackets plus open square brackets table row 1 row 2 end table close square brackets end cell row blank equals cell open square brackets table row 0 cell negative 1 end cell row 1 0 end table close square brackets open square brackets table row cell open parentheses x plus 4 close parentheses minus 1 end cell row cell open parentheses y minus 2 close parentheses minus 2 end cell end table close square brackets plus open square brackets table row 1 row 2 end table close square brackets end cell row blank equals cell open square brackets table row 0 cell negative 1 end cell row 1 0 end table close square brackets open square brackets table row cell x plus 3 end cell row cell y minus 4 end cell end table close square brackets plus open square brackets table row 1 row 2 end table close square brackets end cell row blank equals cell open square brackets table row cell negative y plus 4 end cell row cell x plus 3 end cell end table close square brackets plus open square brackets table row 1 row 2 end table close square brackets end cell row blank equals cell open square brackets table row cell negative y plus 5 end cell row cell x plus 5 end cell end table close square brackets end cell end table end style 

Berdasarkan kesamaan matriks maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell negative y plus 5 end cell equals cell x " left right arrow y equals negative x " plus 5 end cell row cell x plus 5 end cell equals cell y " left right arrow x equals y " minus 5 end cell end table end style 

Subtitusikan begin mathsize 14px style x end style dan begin mathsize 14px style y end style ke persamaan garis

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x plus y minus 2 end cell equals 0 row cell 2 open parentheses y " minus 5 close parentheses plus open parentheses negative x " plus 5 close parentheses minus 2 end cell equals 0 row cell 2 y " minus 10 minus x " plus 5 minus 2 end cell equals 0 row cell 2 y " minus x " minus 7 end cell equals 0 row cell x " minus 2 y " plus 7 end cell equals 0 end table end style 

Jadi, persamaan garis hasil transformasinya adalah begin mathsize 14px style x minus 2 y plus 7 equals 0 end style 

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