Question

Quadrilateral PQRS has points P = (-3,3), Q = (1.-4), R = (5,3), and S = (2,14). Quadrilateral P'Q'R'S' has points P = (-3,-3), Q'= (1,4), R = (5,-3), and S'=(2,-14). What is the transformation of PQRS to P'Q'R'S'?

A. Reflected about the y-axis
B. Rotated 90° clockwise
C. Reflected about the X-axis
D. Rotated 90° counterclockwise

Answer 1

The transformation from PQRS to P'Q'R'S' is a reflection about the X-axis, as each point's y-coordinate changes sign while the x-coordinate remains the same.

Step-by-step explanation:

The transformation from quadrilateral PQRS to P'Q'R'S' involves changing the sign of the y-coordinates while the x-coordinates remain unchanged. This indicates a reflection over the x-axis. When reflecting a figure over the x-axis, each point (x, y) in the figure is transformed to (x, -y). Checking the given coordinates verifies this transformation:

• P = (-3, 3) becomes P' = (-3, -3)
• Q = (1, -4) becomes Q' = (1, 4)
• R = (5, 3) becomes R' = (5, -3)
• S = (2, 14) becomes S' = (2, -14)

Hence, the correct transformation is Reflected about the X-axis (Option C).