Question

write the coordinates of the vertices after a reflection over the line y = x.
r(
,
)
s(
,
)
t(
,
)
u(
,
)

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of each vertex from the graph:

• \( R(-9, 1) \) (since it's at x=-9, y=1)
• \( S(-9, 4) \) (x=-9, y=4)
• \( T(-4, 4) \) (x=-4, y=4)
• \( U(-4, 1) \) (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 is \( (y, x) \).

For \( R(-9, 1) \):

Swap x and y: \( R'(1, -9) \)

For \( S(-9, 4) \):

Swap x and y: \( S'(4, -9) \)

For \( T(-4, 4) \):

Swap x and y: \( T'(4, -4) \)

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

Swap x and y: \( U'(1, -4) \)

Answer:

\( R'(1, -9) \)
\( S'(4, -9) \)
\( T'(4, -4) \)
\( U'(1, -4) \)