Question

select the correct answer.
△abc 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?
o a. a(0,3), b(2,3), c(1,1)
o b. a(0,-3), b(3,-2), c(1,-1)
o c. a(-3,0), b(-3,2), c(-1,1)
o d. a(0,-3), b(-2,-3), c(-1,-1)

Explanation:

Step1: Rotate 180° clockwise about the origin

When a point \((x,y)\) is rotated \(180^{\circ}\) clockwise about the origin, the transformation rule is \((x,y)\to(-x,-y)\).
For \(A(-3,0)\): \((-3,0)\to(3,0)\)
For \(B(-2,3)\): \((-2,3)\to(2,-3)\)
For \(C(-1,1)\): \((-1,1)\to(1,-1)\)

Step2: Reflect across the line \(y = -x\)

When a point \((x,y)\) is reflected across the line \(y=-x\), the transformation rule is \((x,y)\to(-y,-x)\)
For the point obtained from \(A\) after rotation \((3,0)\): \((3,0)\to(0,-3)\)
For the point obtained from \(B\) after rotation \((2,-3)\): \((2,-3)\to(3,-2)\)
For the point obtained from \(C\) after rotation \((1,-1)\): \((1,-1)\to(1,-1)\)

Answer:

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