Question

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

Explanation:

Step1: Find original coordinates

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

• For \( U \): Looking at the grid, it is at \( (-5, 1) \) (since it's 5 units left on the x - axis and 1 unit up on the y - axis).
• For \( V \): It is at \( (-5, 3) \) (5 units left on x, 3 units up on y).
• For \( W \): It is at \( (-2, 5) \) (2 units left on x, 5 units up 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, if we have a point \( (a,b) \), after reflection over \( y = x \), it becomes \( (b,a) \).

• For \( U(-5,1) \): After reflection, the x - coordinate becomes 1 and the y - coordinate becomes - 5. So, \( U'=(1,-5) \).
• For \( V(-5,3) \): After reflection, the x - coordinate becomes 3 and the y - coordinate becomes - 5. So, \( V'=(3,-5) \).
• For \( W(-2,5) \): After reflection, the x - coordinate becomes 5 and the y - coordinate becomes - 2. So, \( W'=(5,-2) \).

Answer:

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