Question

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?


A. A'(0, 3), B'(2, 3), C'(1, 1)



B. A'(0, -3), B'(3, -2), C'(1, -1)



C. A'(-3, 0), B'(-3, 2), C'(-1, 1)



D. A'(0, -3), B'(-2, -3), C'(-1, -1)

Answer 1

Hints:
Rotation \(R_{180}: (x,y)\rightarrow (-x,-y)\)
Reflection \(S_{y=-x}:(x,y)\rightarrow (-y,-x)\)
Transform separately, or combine them:
\(S_{y=-x}\circ R_{180}: (x,y)\rightarrow (y,x)\equiv S_{y=x}\)

For example,
Point (7,1) after rotation of 180 becomes (-7,-1) followed by a reflection about y=-x gives (1,7) as the final position.
Alternatively, using a single reflection about y=x also transforms from (7,1) to (1,7), as explained above.

Answer 2

So Its B?

Answer 3

I don't usually work with letters.
I will be glad to confirm if you post the values represented by option "B".