Question

Identify the correct vertices of the image of triangle RST after a 90° rotation clockwise if the original triangle RST has coordinates R(-1, 1), S(2, -2), and T(-3, 3).

Answer 1

After applying a 90° clockwise rotation to triangle RST with vertices R(-1, 1), S(2, -2), T(-3, 3), the new vertices are R'(1, 1), S'(-2, -2), and T'(3, -3).

Step-by-step explanation:

To determine the vertices of the image of triangle RST after a 90° rotation clockwise, we use the standard rotation formulas given by
x' = x cos θ - y sin θ
y' = x sin θ + y cos θ
where θ is the angle of rotation. In this case, θ is -90° because the rotation is clockwise. Substituting θ with -90° and simplifying, we get
x' = y
y' = -x

Applying this to each vertex, we get:
R' = (y, -x) = (1, 1)
S' = (y, -x) = (-2, -2)
T' = (y, -x) = (3, -3)

Therefore, the coordinates of the vertices of the rotated triangle RST are R'(1, 1), S'(-2, -2), and T'(3, -3).