Question

Angie’s rotation maps triangle XYZ to triangle X’Y’Z’.

X(3, –6) maps to X’(–3, 6)
Y(1, –2) maps to Y’(–1, 2)
Z(–1, –5) maps to Z’(1, 5)

Which describes the rotation?
180 degrees rotation
270 degrees clockwise rotation
90 degrees counterclockwise rotation
90 degrees clockwise rotation

Answer 1

To determine the type of rotation that maps triangle XYZ to triangle X'Y'Z', we can analyze the coordinates of the points before and after the transformation.

Given the points:

- X(3, -6) maps to X'(-3, 6)
- Y(1, -2) maps to Y'(-1, 2)
- Z(-1, -5) maps to Z'(1, 5)

Let's examine the transformation of each point:

1. **Point X(3, -6) to X'(-3, 6)**:
- The original point (3, -6) has its x-coordinate negated and its y-coordinate negated.
- This suggests a 180 degrees rotation.

2. **Point Y(1, -2) to Y'(-1, 2)**:
- The original point (1, -2) also has its x-coordinate negated and its y-coordinate negated.
- This again suggests a 180 degrees rotation.

3. **Point Z(-1, -5) to Z'(1, 5)**:
- The original point (-1, -5) is transformed similarly, with both coordinates negated.
- This continues to suggest a 180 degrees rotation.

Since each point (x, y) transforms to (-x, -y), this transformation corresponds to a rotation of 180 degrees around the origin.

Thus, the answer is **180 degrees rotation**.