Question

write the coordinates of the vertices after a reflection over the x - axis.

Explanation:

Step1: Recall reflection rule

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

Step2: Identify original coordinates

From the graph, point $D$ has coordinates $(-6,-4)$, point $E$ has coordinates $(-6,0)$, point $F$ has coordinates $(-4, - 1)$ and point $G$ has coordinates $(-6,-9)$.

Step3: Apply reflection rule to $D$

For $D(-6,-4)$, after reflection over the $x - axis$, using the rule $(x,y)\to(x, - y)$, we get $D'(-6,4)$.

Step4: Apply reflection rule to $E$

For $E(-6,0)$, after reflection over the $x - axis$, using the rule $(x,y)\to(x, - y)$, we get $E'(-6,0)$.

Step5: Apply reflection rule to $F$

For $F(-4,-1)$, after reflection over the $x - axis$, using the rule $(x,y)\to(x, - y)$, we get $F'(-4,1)$.

Step6: Apply reflection rule to $G$

For $G(-6,-9)$, after reflection over the $x - axis$, using the rule $(x,y)\to(x, - y)$, we get $G'(-6,9)$.

Answer:

$D'(-6,4)$
$E'(-6,0)$
$F'(-4,1)$
$G'(-6,9)$