Question

what transformation transforms (p, q) to (q, p)?

a rotation of 90° about the origin
a reflection over the y - axis
a reflection over the x - axis
a reflection over y = x

Explanation:

A reflection over the line $y = x$ swaps the $x$ - and $y$-coordinates of a point. Given a point $(p,q)$, reflecting it over the line $y = x$ results in the point $(q,p)$. A 90 - degree rotation about the origin transforms $(p,q)$ to $(-q,p)$. A reflection over the $y$-axis changes $(p,q)$ to $(-p,q)$ and a reflection over the $x$-axis changes $(p,q)$ to $(p, - q)$.

Answer:

a reflection over $y = x$