Question

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'?

Answer 1

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

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.