Question

How does the triangle with vertices (-18,2), (8,-17), and (-12,-12) transform when rotated 180° around the origin and then reflected over the line y = -x?

A) (-18,2), (8,-17), and (-12,-12)
B) (18,-2), (-8,17), and (12,12)
C) (18,2), (-8,17), and (12,12)
D) (-18,-2), (8,17), and (-12,12)

Answer 1

After rotating the triangle 180° around the origin and reflecting it over the line y = -x, the transformed vertices are (18,-2), (-8,17), and (12,12), which corresponds to Option B.

Step-by-step explanation:

To solve this question, let's first handle the rotation of the triangle 180° around the origin. This transformation can be performed by changing the sign of both the x and y coordinates of each vertex. Therefore, the vertices after the rotation will be (18, -2), (-8, 17), and (12, 12).

Next, we'll perform the reflection over the line y = -x. To execute this reflection, swap the x and y coordinates of each point, and change their signs because reflecting over y = -x is equivalent to rotating 90° clockwise around the origin and then reflecting over the x-axis. After performing this step, the vertices become:

• The vertex (18, -2) reflects to (2, -18).
• The vertex (-8, 17) reflects to (-17, 8).
• The vertex (12, 12) reflects to (-12, -12).

Therefore, the correct transformation is Option B: (18,-2), (-8,17), and (12,12).