The coordinates of pqr are p(1, 1), q(2, 2), and r(3, 1). if pqr is rotated 90° about the origin, what are the vertices of p'q'r'?

(-1, 1), (-2, 2), and (-1, 3)

Step-by-step explanation:

The formula for rotation of a point (x,y) by an angle θ about the origin is  

x' = xcosθ  -  ysinθ

y' = ycosθ + xsinθ

If θ = 90°, sinθ = 1 and cosθ = 0, and the formula becomes

x' = -y

y' =  x

P: (1, 1)   ⟶ (-1,  1)

Q:(2, 2) ⟶ (-2, 2)

R: (3, 1) ⟶  (-1,  3)  

The vertices of P'Q'R' are (-1, 1), (-2, 2), and (-1, 3).

The Figure below shows the triangle before and after the rotation.