Problem:
Triangle OAB has O=(0,0),B=(5,0), and A in the first quadrant. In addition, ∠ABO=90∘ and ∠AOB=30∘. Suppose that OA is rotated 90∘ counterclockwise about O. What are the coordinates of the image of A?
Answer Choices:
A. (−3103,5)
B. (−353,5)
C. (3,5)
D. (353,5)
E. (3103,5)
Solution:
Because △OAB is a 30−60−90∘ triangle, we have BA=353. Let A′ and B′ be the images of A and B, respectively, under the rotation. Then B′=(0,5),B′A′ is horizontal, and B′A′=BA=353. Hence A′ is in the second quadrant and