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’?

Answer 1

To find the coordinates of Q' after rotating Triangle PQR 90° counterclockwise about the origin, we can use the rotation formula x' = x*cos(θ) - y*sin(θ) and y' = x*sin(θ) + y*cos(θ). Plugging in the coordinates of Q(-6, -8) and θ = 90°, we find that the coordinates of Q' are (8, -6).

Step-by-step explanation:

Triangle PQR will be rotated 90° counterclockwise about the origin.

To find the coordinates of Q' after the rotation, we can apply the rotation formula:

x' = x*cos(θ) - y*sin(θ)

y' = x*sin(θ) + y*cos(θ)

Plugging in the coordinates of Q(-6, -8) and θ = 90°, we can calculate:
x' = -6*cos(90°) - (-8)*sin(90°) = -6*0 - (-8)*1 = 8

y' = -6*sin(90°) + (-8)*cos(90°) = -6*1 + (-8)*0 = -6

Thus, the coordinates of Q' are (8, -6).