Question

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

Explanation:

Step1: Identify original coordinates

First, find the original coordinates of points \( R \), \( U \), and \( V \) from the graph.

• For \( U \): Looking at the graph, \( U \) is at \( (3, 0) \) (since it's 3 units right on the x - axis and 0 on the y - axis).
• For \( R \): \( R \) is at \( (2, - 6) \) (2 units right on x, 6 units down on y).
• For \( V \): \( V \) is at \( (5, - 8) \) (5 units right on x, 8 units down on y).

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

The rule for reflecting a point \( (x,y) \) over the line \( y=x \) is to swap the x - coordinate and the y - coordinate. So the new coordinates \( (x',y') \) after reflection are given by \( (y,x) \).

• For point \( U=(3,0) \): After reflection over \( y = x \), the new coordinates \( U'=(0,3) \) (swap x and y: \( x' = 0,y'=3 \)).
• For point \( R=(2, - 6) \): After reflection over \( y = x \), the new coordinates \( R'=(-6,2) \) (swap x and y: \( x'=-6,y' = 2 \)).
• For point \( V=(5, - 8) \): After reflection over \( y = x \), the new coordinates \( V'=(-8,5) \) (swap x and y: \( x'=-8,y' = 5 \)).

Answer:

\( R(-6,2) \), \( U(0,3) \), \( V(-8,5) \)