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 $(0, 8)$
• $T$ is at $(7, 5)$ (assuming the x - coordinate of T is 7, since it's 7 units from the y - axis, and y - coordinate is 5)
• $U$ is at $(7, 10)$ (x - coordinate 7, y - coordinate 10)

Step2: Apply reflection over x - axis rule

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

• For point $V(0,8)$: After reflection, $V'=(0, - 8)$
• For point $T(7,5)$: After reflection, $T'=(7, - 5)$
• For point $U(7,10)$: After reflection, $U'=(7, - 10)$

Step3: Graph the new points

Plot the points $V'(0, - 8)$, $T'(7, - 5)$ and $U'(7, - 10)$ 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 $V'(0, - 8)$, $T'(7, - 5)$ and $U'(7, - 10)$. (To graph, plot these points and connect them.)