Question

graph the image of parallelogram pqrs after a reflection over the line y = -x.

Explanation:

Step1: Identify coordinates

Find coordinates of \( P, Q, R, S \). From graph:
\( P(2, 1) \), \( Q(2, 8) \), \( R(5, 10) \), \( S(5, 3) \).

Step2: Apply reflection rule

Reflection over \( y = -x \) transforms \( (x, y) \) to \( (-y, -x) \).

• \( P(2, 1) \to P'(-1, -2) \)
• \( Q(2, 8) \to Q'(-8, -2) \)
• \( R(5, 10) \to R'(-10, -5) \)
• \( S(5, 3) \to S'(-3, -5) \)

Step3: Plot reflected points

Plot \( P'(-1, -2) \), \( Q'(-8, -2) \), \( R'(-10, -5) \), \( S'(-3, -5) \) and connect to form the image.

Answer:

The image of parallelogram \( PQRS \) after reflection over \( y = -x \) has vertices at \( P'(-1, -2) \), \( Q'(-8, -2) \), \( R'(-10, -5) \), \( S'(-3, -5) \) (graph plotted by connecting these points).