Math Gold Medalist

Lor

2023 AMC 10A 

Problem 19

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 $|r-s|$?

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

Coordinate Geometry

Rotation

Slope of a Line

Equation of a Line

Drawing

P=Centre of Rotation

P lies on perpendicular bisector of AA’ and BB’

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   Solution