How to Find the Center and Angle of Rotation Mapping Triangle A to Triangle B

Question

Describe each rotation fully. Identify the centre (x,y) of rotation and the angle of rotation that maps triangle A to triangle B. For the angle, type 90c (clockwise) or 90a (counter-clockwise/anti-clockwise).

Accepted Answer

centre (0,0), angle 90c

Answer

Step 1: Identify corresponding vertices of triangle A and triangle B. For example, take the top vertex of A at (-3,4), the right vertex of A at (-2,4), and the left vertex of A at (-3,1). The corresponding vertices of B are (4,2), (4,3), and (1,3). Step 2: Test the rotation rule for 90 degrees clockwise about the origin (0,0): (x,y) → (y,-x). Apply this to the top vertex of A (-3,4): (4, 3), which matches the right vertex of B. Apply it to (-2,4): (4,2), which matches the top vertex of B. Apply it to (-3,1): (1,3), which matches the bottom vertex of B. Step 3: Verify the center of rotation. Since the rotation rule about the origin perfectly maps all vertices of A to B, the center is (0,0). The direction is clockwise, so the angle is 90c.