Triangle ABC is drawn with vertices at A(−1, −4), B(−6, −6), C(−4, −2). After a rotation, image A′B′C′ has vertices A′(−4, 1), B′(−6, 6), C′(−2, 4).

Question

Triangle ABC is drawn with vertices at A(−1, −4), B(−6, −6), C(−4, −2). After a rotation, image A′B′C′ has vertices A′(−4, 1), B′(−6, 6), C′(−2, 4).

Part A: Determine the two different rotations that would create the image. (1 point)

Part B: Explain how you know your answer to Part A is correct. (3 points

Answer 1

Part A: The two different rotations that could create the image are a 90-degree counterclockwise rotation and a 270-degree clockwise rotation.

Part B: We know this answer is correct because a 90-degree counterclockwise rotation would switch the x and y coordinates and negate the new y coordinates, which matches the new coordinates of the image triangle. Additionally, a 270-degree clockwise rotation would also match the new coordinates of the image triangle as it would switch the x and y coordinates and negate the new x coordinates. Therefore, both rotations would result in the correct image triangle with the given vertices.