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anonymous
 one year ago
ΔABC with vertices A(3, 0), B(2, 3), C(1, 1) is rotated 180° clockwise about the origin. It is then reflected across the line y = x. What are the coordinates of the vertices of the image?
anonymous
 one year ago
ΔABC with vertices A(3, 0), B(2, 3), C(1, 1) is rotated 180° clockwise about the origin. It is then reflected across the line y = x. What are the coordinates of the vertices of the image?

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LynFran
 one year ago
Best ResponseYou've already chosen the best response.1ok so dw:1435524695372:dw

LynFran
 one year ago
Best ResponseYou've already chosen the best response.1the imag of B would be (3,2) ...did u get that?

LynFran
 one year ago
Best ResponseYou've already chosen the best response.1And the image of C would be (1,1)...did u get that?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0hint: \(R_{180}: (x,y)>(x,y)\) or premultiply by the first matix given by @lynfran \(s_{y=x}: (x,y)>(y,x)\) or premultiply by the second matrix. If you combine the two, you have \(s_{y=x} \circ R_{180}: (x,y) > (y,x)\), the equivalent of \(s_{y=x}\) or reflection about y=x. Using matrices, \[\left[\begin{matrix}0 & 1 \\ 1 & 0\end{matrix}\right]\left[\begin{matrix}1 & 0 \\ 0 & 1\end{matrix}\right]=\left[\begin{matrix}0 & 1 \\ 1 & 0\end{matrix}\right]\] Say a vertex has coordinates (2,1) The transformed coordinates would be (y,x)=(1,2) Using the combined matrix, \(\left[\begin{matrix}0 & 1\\1 & 0\end{matrix}\right]\left[\begin{matrix}2\\1 \end{matrix}\right]=\left[\begin{matrix}1\\2\end{matrix}\right]\), or (1,2) as before.
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