Question

Use the graph to answer the question.

graph of triangle ABC with vertices at negative 2 comma negative 2, 3 comma 3, 2 comma negative 5

Determine the coordinates of triangle A′B′C′ if triangle ABC is rotated 270° clockwise.
A′(−2, 2), B′(3, −3), C′(−5, −2)
A′(2, −2), B′(−3, 3), C′(5, 2)
A′(2, 2), B′(−3, −3), C′(5, −2)
A′(2, −2), B′(−3, 3), C′(2, 5)

Answer 1

To determine the coordinates of triangle A′B′C′ after triangle ABC is rotated 270° clockwise, we can apply the general transformation rules for rotation.

A point (x, y) when rotated 270° clockwise (or equivalently 90° counterclockwise) transforms to (y, -x).

Let's find the new coordinates for each vertex of triangle ABC:

1. **Vertex A (-2, -2)**:
- Rotate 270° clockwise:
\[
A' = (-2, -2) \rightarrow A' = (-2, 2)
\]

2. **Vertex B (3, 3)**:
- Rotate 270° clockwise:
\[
B' = (3, 3) \rightarrow B' = (3, -3)
\]

3. **Vertex C (2, -5)**:
- Rotate 270° clockwise:
\[
C' = (2, -5) \rightarrow C' = (-5, -2)
\]

Now we have the new coordinates:
- A′(−2, 2)
- B′(3, −3)
- C′(−5, −2)

The correct answer matches the first option:
**A′(−2, 2), B′(3, −3), C′(−5, −2)**