Question

graph the image of parallelogram tuvw after a reflection over the line y = -2.

Explanation:

Step1: Recall reflection rule

For a point $(x,y)$ reflected over the line $y = k$, the new - point is $(x,2k - y)$. Here $k=-2$.

Step2: Find coordinates of reflected points

• Point $T(-5,0)$: Using the formula $(x,2k - y)$, we have $x=-5$ and $2\times(-2)-0=-4$. So the new point $T'$ is $(-5,-4)$.
• Point $U(2,0)$: With $x = 2$ and $2\times(-2)-0=-4$. So the new point $U'$ is $(2,-4)$.
• Point $V(3,6)$: Here $x = 3$ and $2\times(-2)-6=-4 - 6=-10$. So the new point $V'$ is $(3,-10)$.
• Point $W(-4,6)$: For $x=-4$ and $2\times(-2)-6=-4 - 6=-10$. So the new point $W'$ is $(-4,-10)$.

Step3: Graph the new parallelogram

Plot the points $T'(-5,-4)$, $U'(2,-4)$, $V'(3,-10)$ and $W'(-4,-10)$ and connect them in order to form the reflected parallelogram.

Answer:

Graph the points $T'(-5,-4)$, $U'(2,-4)$, $V'(3,-10)$ and $W'(-4,-10)$ and connect them to get the reflected parallelogram.