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Difference between revisions of "2021 AMC 12B Problems/Problem 5"

(Created page with "The 2021 AMC 12B will be held on February 10th, 2021. The problems will not be made public until 24 hours after that.")
 
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The 2021 AMC 12B will be held on February 10th, 2021. The problems will not be made public until 24 hours after that.
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==Problem==
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The point <math>P(a,b)</math> in the <math>xy</math>-plane is first rotated counterclockwise by <math>90\deg</math> around the point <math>(1,5)</math> and then reflected about the line <math>y = -x</math>. The image of <math>P</math> after these two transformations is at <math>(-6,3)</math>. What is <math>b - a ?</math>
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<math>\textbf{(A)} ~1 \qquad\textbf{(B)} ~3 \qquad\textbf{(C)} ~5 \qquad\textbf{(D)} ~7 \qquad\textbf{(E)} ~9</math>
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==Solution==
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<math>\boxed{\textbf{(D)} ~7}</math>

Revision as of 17:41, 11 February 2021

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

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

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