## A community for students. Sign up today

Here's the question you clicked on:

## 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?

• This Question is Open
1. LynFran

ok so |dw:1435524695372:dw|

2. LynFran

the imag of B would be (3,-2) ...did u get that?

3. LynFran

And the image of C would be (1,-1)...did u get that?

4. mathmate

hint: $$R_{180}: (x,y)->(-x,-y)$$ 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.

#### Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy