Chapter 11.3, Problem 30E

To determine

To explain: Whether the friend is correct or not.

Explanation of Solution

Given information: The friend claims that rotating a figure by ${180}^{°}$ is the same as reflecting a figure in the $y$ -axis and then reflecting it in the $x$ -axis

Calculation:

Let $\left(p,q\right)$ be the point of given figure. The rotation is about $180$ thus, the point become $\left(-p,-q\right)$ . The point after reflection in y-axis is $\left(-p,q\right)$ and the point after reflection in x-axis is $\left(-p,-q\right)$ .

Since, the point in the image after transformation in both the case is same, the friend if right.