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 each vertex from the graph:

• \( K(-4, 2) \)
• \( L(2, 2) \)
• \( M(2, 10) \)
• \( N(-4, 10) \)

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 \( K(-4, 2) \):

Swap \( x \) and \( y \): \( K'(2, -4) \)

For \( L(2, 2) \):

Swap \( x \) and \( y \): \( L'(2, 2) \) (since \( x = y \), the point remains the same)

For \( M(2, 10) \):

Swap \( x \) and \( y \): \( M'(10, 2) \)

For \( N(-4, 10) \):

Swap \( x \) and \( y \): \( N'(10, -4) \)

Answer:

\( K'(2, -4) \)
\( L'(2, 2) \)
\( M'(10, 2) \)
\( N'(10, -4) \)