Question

graph the image of △stu after a reflection over the line y = -2.

Explanation:

Step1: Recall reflection rule

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

Step2: Identify coordinates of $\triangle STU$

Assume $S(3,2)$, $T(3,4)$, $U(6,4)$.

Step3: Calculate reflected coordinates of $S$

For $S(3,2)$ with $k = - 2$, the new $y$ - coordinate is $2\times(-2)-2=-4 - 2=-6$, and the $x$ - coordinate remains the same. So $S'$ is $(3,-6)$.

Step4: Calculate reflected coordinates of $T$

For $T(3,4)$ with $k=-2$, the new $y$ - coordinate is $2\times(-2)-4=-4 - 4=-8$, and the $x$ - coordinate remains the same. So $T'$ is $(3,-8)$.

Step5: Calculate reflected coordinates of $U$

For $U(6,4)$ with $k = - 2$, the new $y$ - coordinate is $2\times(-2)-4=-4 - 4=-8$, and the $x$ - coordinate remains the same. So $U'$ is $(6,-8)$.

Step6: Graph the new triangle

Plot the points $S'(3,-6)$, $T'(3,-8)$, $U'(6,-8)$ and connect them to form the reflected $\triangle S'T'U'$.

Answer:

Graph the points $S'(3,-6)$, $T'(3,-8)$, $U'(6,-8)$ and connect them to get the image of $\triangle STU$ after reflection over the line $y=-2$.