2021 AMC 12B Problems/Problem 5

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 $b - a ?$

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

Solution

$\boxed{\textbf{(D)} ~7}$

Video Solution by OmegaLearn (Rotation & Reflection tricks)

https://youtu.be/VyRWjgGIsRQ

~ pi_is_3.14

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2021 AMC 12B Problems/Problem 5

Problem

Solution

Video Solution by OmegaLearn (Rotation & Reflection tricks)