The problem asks for the image of the point $(-7, 2)$ under a rotation of $180^\circ$ about the origin.

1. Problem Description

The problem asks for the image of the point $(-7, 2)$ under a rotation of $180^\circ$ about the origin.

2. Solution Steps

A rotation of $180^\circ$ about the origin maps a point $(x, y)$ to the point $(-x, -y)$.

So, the point $(-7, 2)$ will be mapped to $(-(-7), -2)$, which is $(7, -2)$.

3. Final Answer

(7, -2)