Question

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

Explanation:

Step1: Find coordinates of vertices

First, identify the coordinates of \( T \), \( U \), and \( V \) from the graph.

• \( V \) is at \( (0, 8) \)
• \( T \) is at \( (7, 5) \) (assuming the grid, since from x=0 to x=7 and y=8 to y=5? Wait, looking at the graph: U is at (7,10)? Wait no, the grid: let's check again. The y-axis: V is on (0,8), U is at (7,10)? Wait the graph: U is at (7,10)? Wait the y-axis has 10 at the top. Wait, the points:
• \( V \): (0, 8) (on y-axis, y=8)
• \( U \): (7, 10) (since x=7, y=10)
• \( T \): (7, 5) (x=7, y=5)

Step2: Apply reflection over x-axis

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

• For \( V(0, 8) \): Reflect to \( V'(0, -8) \)
• For \( U(7, 10) \): Reflect to \( U'(7, -10) \)
• For \( T(7, 5) \): Reflect to \( T'(7, -5) \)

Step3: Plot the reflected points

Plot \( V'(0, -8) \), \( U'(7, -10) \), 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.)