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2021 AMC 10B Problems/Problem 9

Revision as of 17:38, 11 February 2021 by Bjc (talk | contribs)

Problem

The point $P(a,b)$ in the $xy$-plane is first rotated counterclockwise by $90\deg$ around the point $(1,5)$ and then reflected about the line $y = -x$. The image of $P$ after these two transformations is at $(-6,3)$. What is $b - a ?$

$\textbf{(A)} ~1 \qquad\textbf{(B)} ~3 \qquad\textbf{(C)} ~5 \qquad\textbf{(D)} ~7 \qquad\textbf{(E)} ~9$

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