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 $(7, 10)$ (assuming the grid, since from x=0 to x=7 and y=0 to y=10)
• $T$ is at $(7, 5)$

Step2: Apply reflection over x - axis rule

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

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

Step3: Graph the new 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 reflected triangle $\triangle T'U'V'$ has vertices at $V'(0, - 8)$, $U'(7, - 10)$ and $T'(7, - 5)$ (and is graphed by plotting these points and connecting them).