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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)

1 answer

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)