Question

find the image of b for a counterclockwise rotation of 180° about its center. a. point b b. point d c. point a d. point c

Explanation:

Step1: Recall 180° rotation property

A 180° rotation about a center (assuming a quadrilateral or symmetric figure, like a square/rectangle with vertices A, B, C, D) means that a point \( (x,y) \) rotates to \( (-x,-y) \) about the center, or in a symmetric figure, the image of a vertex is the one diagonally opposite. For a figure with vertices B and D being opposite (e.g., square/rectangle), rotating B 180° counterclockwise about the center will map it to D.

Step2: Identify the symmetric pair

In a typical quadrilateral (like square, rectangle) with vertices A, B, C, D in order, a 180° rotation about the center swaps B with D (and A with C). So the image of B under 180° counterclockwise rotation about the center is D.

Answer:

B. point D