Question

A 90° rotation around the origin followed by a reflection across the line x = 3 maps △JKL, with coordinates J(–2, 2), K(–2, 6), and L(–8, 2), to △PQR. Find the area of △PQR.

Answer 1

Answer: A 90° rotation around the origin maps point (x, y) to (-y, x). So, the image of point J after a 90° rotation is J' = (-2, 2) -> (-2, -2).

A reflection across the line x = 3 maps point (x, y) to (2x - 3, y). So, the image of point J' after a reflection across x = 3 is J'' = (-2, -2) -> (4, -2).

Similarly, we can find the images of K and L:

K' = (-2, 6) -> (-6, -2)

K'' = (-6, -2) -> (-2, -2)

L' = (-8, 2) -> (2, -8)

L'' = (2, -8) -> (8, -2)

Therefore, the image of triangle JKL after the 90° rotation and reflection is triangle PQR, with vertices P = J'', Q = K'', and R = L''.

The area of triangle PQR can be found using the Shoelace Formula:

P = [(4 -2) + (-2 -2) + (8 -2) * (-2 - (-8))]/2 = [6 + 4 * 6]/2 = 30/2 = 15 square units.

So, the area of triangle PQR is 15 square units.

Explanation: