Question

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

Explanation:

Step1: Recall reflection rule

When reflecting a point $(x,y)$ over the $x -$axis, the transformation rule is $(x,y)\to(x, - y)$.

Step2: Identify coordinates of $\triangle QRS$

Let's assume $Q=(0,-4)$, $R=( - 1,-2)$, $S=(8,-2)$.

Step3: Apply reflection rule to $Q$

For $Q=(0,-4)$, after reflection over the $x -$axis, $Q'=(0,4)$ since $x = 0$ and $y=-(-4)=4$.

Step4: Apply reflection rule to $R$

For $R=( - 1,-2)$, after reflection over the $x -$axis, $R'=( - 1,2)$ since $x=-1$ and $y=-(-2)=2$.

Step5: Apply reflection rule to $S$

For $S=(8,-2)$, after reflection over the $x -$axis, $S'=(8,2)$ since $x = 8$ and $y=-(-2)=2$.

Step6: Graph the new triangle

Plot the points $Q'(0,4)$, $R'(-1,2)$ and $S'(8,2)$ on the coordinate - plane and connect them to form $\triangle Q'R'S'$.

Answer:

Graph the points $Q'(0,4)$, $R'(-1,2)$ and $S'(8,2)$ and connect them to form the reflected triangle.