tentukan bayangan segitiga abc jika ddiketahui a(-1,-2) , b(7,-2) , c(7,4) dirotasi dengan pusat (-1,5) dan sudut putar 90 ?

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tentukan bayangan segitiga abc jika ddiketahui a(-1,-2) , b(7,-2) , c(7,4) dirotasi dengan pusat (-1,5) dan sudut putar 90 ?

Jawaban Terkonfirmasi

begin{pmatrix} x'\ y' end{pmatrix} =begin{pmatrix} cos theta &-sin theta \ sintheta & cos theta end{pmatrix} begin{pmatrix} x-a\ y-b end{pmatrix} +begin{pmatrix} a\ b end{pmatrix}
begin{pmatrix} x'\ y' end{pmatrix} =begin{pmatrix} cos 90^{circ} &-sin 90^{circ} \ sin90^{circ} & cos 90^{circ} end{pmatrix} begin{pmatrix} x+1\ y-5 end{pmatrix} +begin{pmatrix} -1\ 5 end{pmatrix}
begin{pmatrix} x'\ y' end{pmatrix} =begin{pmatrix} 0 &-1 \ 1 & 0 end{pmatrix} begin{pmatrix} x+1\ y-5 end{pmatrix} +begin{pmatrix} -1\ 5 end{pmatrix}
begin{pmatrix} x'\ y' end{pmatrix} = begin{pmatrix} -y+6\ x+6 end{pmatrix}
K(x,y)overset{R[P(-1,5),90^{circ}]}{rightarrow}K'(-y+6,x+6)

A(-1,-2)overset{R[P(-1,5),90^{circ}]}{rightarrow}A'(2+6,-1+6)=A'(8,5)
B(7,-2)overset{R[P(-1,5),90^{circ}]}{rightarrow}B'(2+6,7+6)=B'(8,13)
C(7,4)overset{R[P(-1,5),90^{circ}]}{rightarrow}C'(-4+6,7+6)=C'(2,13)