Question

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

Explanation:

Step1: Identify original coordinates

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

• \( V \) is at \( (0, 8) \)
• \( U \) is at \( (8, 10) \)
• \( T \) is at \( (8, 5) \)

Step2: Apply reflection over x - axis rule

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

• For \( V(0, 8) \): After reflection, \( V' = (0, -8) \) (since \( x = 0 \), \( y=-8 \))
• For \( U(8, 10) \): After reflection, \( U'=(8, - 10) \) (since \( x = 8 \), \( y = - 10\))
• For \( T(8, 5) \): After reflection, \( T'=(8, - 5) \) (since \( x = 8 \), \( y=-5\))

Step3: Graph the new points

Plot the points \( V'(0, -8) \), \( U'(8, -10) \), and \( T'(8, -5) \) 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 \( V'(0, -8) \), \( U'(8, -10) \), and \( T'(8, -5) \). (To graph, plot these points and connect them.)