Question

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

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of \( Q \), \( R \), and \( S \) from the graph.

• For \( Q \): Looking at the grid, \( Q \) is at \( (2, 5) \) (x=2, y=5).
• For \( R \): \( R \) is at \( (2, 9) \) (x=2, y=9).
• For \( S \): \( S \) is at \( (-8, 7) \) (x=-8, y=7).

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 \( Q(2, 5) \): Swap x and y: \( Q' = (5, 2) \).
• For \( R(2, 9) \): Swap x and y: \( R' = (9, 2) \).
• For \( S(-8, 7) \): Swap x and y: \( S' = (7, -8) \).

Answer:

\( Q'(5, 2) \)
\( R'(9, 2) \)
\( S'(7, -8) \)