Question

Quadrilateral PQRS, with vertex P(-5, -3), undergoes a transformation to form quadrilateral P′Q′R′S′, with P′ at (5, 3). The type of transformation PQRS undergoes is a ________

A. reflection over the X-axis
B. reflection over the Y-axis
C. translation 2 units right and 7 units up.
D. 180 degrees about the origin.

Answer 1

D

Explanation:

Answer 2

D. 180 degrees about the origin.

Explanation:

Let's consider what these transformation choices do.

A. Reflection over the X-axis changes the sign of the Y-coordinate. (-5, -3) becomes (-5, 3).

B. Reflection over the Y-axis changes the sign of the X-coordinate. (-5, -3) becomes (5, -3).

Reflection over both axes changes the signs of both X- and Y-coordinates, so (-5, -3) would become (5, 3). That is, one choice for the desired transformation is "A and B".

C. Translation 2 right and 7 up adds (2, 7) to the coordinates, so (-5, -3) becomes (-3, 4).

D. Rotation 180° about the origin changes the signs of both X- and Y-coordinates, so (-5, -3) becomes (5, 3). This is an appropriate single choice for the desired transformation.