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2021 AMC 12B Question 5

AMC12 · 2021 AMC 12B

Question 5

The point $P(a,b)$ in the $xy$-plane is first rotated counterclockwise by $90^\circ$ 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 $b-a?$
  1. $1$
  2. $3$
  3. $5$
  4. $7$
  5. $9$