Question

write the coordinates of the vertices after a reflection over the line y = x.
u(\boxed{\quad}, \boxed{\quad})
v(\boxed{\quad}, \boxed{\quad})
w(\boxed{\quad}, \boxed{\quad})

Explanation:

Step1: Find original coordinates

First, determine the original coordinates of \( U \), \( V \), and \( W \) from the graph.

• \( U \): \( (-5, 1) \) (x = -5, y = 1)
• \( V \): \( (-5, 3) \) (x = -5, y = 3)
• \( W \): \( (-2, 5) \) (x = -2, y = 5)

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, resulting in \( (y, x) \).

• For \( U(-5, 1) \):

Swap \( x \) and \( y \): \( U' = (1, -5) \)

• For \( V(-5, 3) \):

Swap \( x \) and \( y \): \( V' = (3, -5) \)

• For \( W(-2, 5) \):

Swap \( x \) and \( y \): \( W' = (5, -2) \)

Answer:

\( U'(1, -5) \)
\( V'(3, -5) \)
\( W'(5, -2) \)