Question

write the coordinates of the vertices after a reflection over the line y = x.

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of points \( P \), \( Q \), \( R \), \( S \) from the graph:

• \( P(0, -9) \) (since it's on the y - axis, x = 0, y=-9)
• \( Q(2, -9) \) (x = 2, y=-9)
• \( R(6, -1) \) (x = 6, y=-1)
• \( S(4, -1) \) (x = 4, y=-1)

Step2: Apply reflection over \( y = x \)

The rule for reflecting a point \( (x, y) \) over the line \( y=x \) is to swap the x - and y - coordinates, so the new point \( (x', y')=(y, x) \).

For \( P(0, -9) \):

Using the reflection rule, \( P'( - 9,0) \) (swap x = 0 and y=-9).

For \( Q(2, -9) \):

Using the reflection rule, \( Q'( - 9,2) \) (swap x = 2 and y=-9).

For \( R(6, -1) \):

Using the reflection rule, \( R'( - 1,6) \) (swap x = 6 and y=-1).

For \( S(4, -1) \):

Using the reflection rule, \( S'( - 1,4) \) (swap x = 4 and y=-1).

Answer:

\( P'(-9, 0) \)
\( Q'(-9, 2) \)
\( R'(-1, 6) \)
\( S'(-1, 4) \)