Question

graph the image of square tuvw after a reflection over the y-axis.

Explanation:

Step1: Find coordinates of T, U, V, W

From the graph:

• \( T(-6, 4) \)
• \( U(-2, 4) \)
• \( V(-2, 8) \)
• \( W(-6, 8) \)

Step2: Apply reflection over y - axis

The rule for reflection over the \( y \) - axis is \( (x,y)\to(-x,y) \).

• For \( T(-6, 4) \): New point \( T'(6, 4) \) (since \( -(-6)=6 \), \( y = 4 \) remains)
• For \( U(-2, 4) \): New point \( U'(2, 4) \) (since \( -(-2)=2 \), \( y = 4 \) remains)
• For \( V(-2, 8) \): New point \( V'(2, 8) \) (since \( -(-2)=2 \), \( y = 8 \) remains)
• For \( W(-6, 8) \): New point \( W'(6, 8) \) (since \( -(-6)=6 \), \( y = 8 \) remains)

Step3: Plot the new points

Plot \( T'(6, 4) \), \( U'(2, 4) \), \( V'(2, 8) \), \( W'(6, 8) \) and connect them to form the reflected square.

Answer:

The reflected square has vertices at \( T'(6, 4) \), \( U'(2, 4) \), \( V'(2, 8) \), \( W'(6, 8) \) (graph by plotting these points and connecting them).