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2008 AMC 10A Problem 19

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2008 AMC 10A Problem 19AMC 10 Step by Step

Name: Date: September 13, 2026

Transformations & Symmetry · difficulty 4 of 5 · about 5 min · position P16-20

Rectangle $PQRS$ lies in a plane with $PQ=RS=2$ and $QR=SP=6$ . The rectangle is rotated $90^\circ$ clockwise about $R$ , then rotated $90^\circ$ clockwise about the point $S$ moved to after the first rotation. What is the length of the path traveled by point $P$ ?

A)
$\left(2\sqrt{3}+\sqrt{5}\right)\pi$
B)
$6\pi$
C)
$\left(3+\sqrt{10}\right)\pi$
D)
$\left(\sqrt{3}+2\sqrt{5}\right)\pi$
E)
$2\sqrt{10}\pi$

2008 AMC 10A Problem 19

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