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2008 AMC 10B Problem 14

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2008 AMC 10B Problem 14AMC 10 Step by Step

Name: Date: September 13, 2026

Coordinate Geometry · difficulty 2 of 5 · about 3 min · position P11-15

Triangle $OAB$ has $O=(0,0)$ , $B=(5,0)$ , and $A$ in the first quadrant. In addition, $\angle ABO=90^\circ$ and $\angle AOB=30^\circ$ . Suppose that $OA$ is rotated $90^\circ$ counterclockwise about $O$ . What are the coordinates of the image of $A$ ?

A)
$\left( - \frac {10}{3}\sqrt {3},5\right)$
B)
$\left( - \frac {5}{3}\sqrt {3},5\right)$
C)
$\left(\sqrt {3},5\right)$
D)
$\left(\frac {5}{3}\sqrt {3},5\right)$
E)
$\left(\frac {10}{3}\sqrt {3},5\right)$

2008 AMC 10B Problem 14

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