Question

graph the image of △tuv after a reflection over the x-axis.

Explanation:

Step1: Find coordinates of T, U, V

From the graph:

• \( T(-4, -6) \)
• \( U(4, -6) \)
• \( V(-3, -8) \)

Step2: Apply reflection over x - axis rule

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

• For \( T(-4, -6) \): New coordinates \( T'(-4, -(-6)) = (-4, 6) \)
• For \( U(4, -6) \): New coordinates \( U'(4, -(-6)) = (4, 6) \)
• For \( V(-3, -8) \): New coordinates \( V'(-3, -(-8)) = (-3, 8) \)

Step3: Plot the new points

Plot \( T'(-4, 6) \), \( U'(4, 6) \), and \( V'(-3, 8) \) on the coordinate plane and connect them to form the reflected triangle.

Answer:

The image of \( \triangle TUV \) after reflection over the x - axis has vertices \( T'(-4, 6) \), \( U'(4, 6) \), and \( V'(-3, 8) \). (The graph should have these three points connected to form the triangle.)