Question

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

Explanation:

Step1: Find coordinates of vertices

First, identify the coordinates of \( \triangle TUV \). From the graph:

• \( V \) is at \( (0, 8) \)
• \( U \) is at \( (7, 10) \) (assuming the grid, since it's 7 units right on x and 10 up on y)
• \( T \) is at \( (7, 5) \)

Step2: Apply reflection over x - axis rule

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

• For \( V(0, 8) \): Applying the rule, the image \( V' \) is \( (0, - 8) \)
• For \( U(7, 10) \): Applying the rule, the image \( U' \) is \( (7, - 10) \)
• For \( T(7, 5) \): Applying the rule, the image \( T' \) is \( (7, - 5) \)

Step3: Plot the reflected points

Plot the points \( V'(0, - 8) \), \( U'(7, - 10) \), and \( T'(7, - 5) \) on the coordinate plane and connect them to form the reflected triangle \( \triangle T'U'V' \).

Answer:

The image of \( \triangle TUV \) after reflection over the x - axis has vertices at \( V'(0, - 8) \), \( U'(7, - 10) \), and \( T'(7, - 5) \). (To graph, plot these points and connect them.)