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Difference between revisions of "2023 AMC 10A Problems/Problem 19"

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The line segment formed by <math>A(1, 2)</math> and <math>B(3, 3)</math> is rotated to the line segment formed by <math>A'(3, 1)</math> and <math>B'(4, 3)</math> about the point <math>P(r, s)</math>. What is <math>|r-s|</math>?
  
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<math>\text{A) } \frac{1}{4} \qquad \text{B) } \frac{1}{2} \qquad \text{C) } \frac{3}{4}  \qquad \text{D) } \frac{2}{3} \qquad  \text{E) } 1</math>

Revision as of 15:03, 9 November 2023

The line segment formed by $A(1, 2)$ and $B(3, 3)$ is rotated to the line segment formed by $A'(3, 1)$ and $B'(4, 3)$ about the point $P(r, s)$. What is $|r-s|$?

$\text{A) } \frac{1}{4} \qquad \text{B) } \frac{1}{2} \qquad \text{C) } \frac{3}{4} \qquad \text{D) } \frac{2}{3} \qquad \text{E) } 1$

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