Question

Triangle PQR has vertices at P(–3, –2), Q(5, –6), and R(–1, 4). Triangle PQR will be rotated 90° counterclockwise about the origin. What will be the coordinates of Q′?

A. (–6, –5)
B. (–5, –6)
C. (5, 6)
D. (6, 5)

Answer 1

The coordinates of point Q' after rotating triangle PQR 90° counterclockwise about the origin are (6, 5).

Step-by-step explanation:

To rotate a point counterclockwise about the origin, we can use the rotation formulas:

• x' = x · cos(θ) - y · sin(θ)
• y' = x · sin(θ) + y · cos(θ)

For point Q(5, -6), when we rotate it 90° counterclockwise, the new coordinates, Q', would be:

• x' = 5 · cos(90°) - (-6) · sin(90°) = 0 - (-6) = 6
• y' = 5 · sin(90°) + (-6) · cos(90°) = 5 + 0 = 5

Hence, the coordinates of Q' are (6, 5).