Question

write the coordinates of the vertices after a reflection over the line y = 3.

Explanation:

Step1: Recall reflection rule

For a reflection over the horizontal line $y = k$, the $x$-coordinate of a point $(x,y)$ remains the same, and the new $y$-coordinate is given by $y'=2k - y$. Here $k = 3$.

Step2: Find coordinates of $D$

The coordinates of $D$ are $(-4,3)$. Using the formula $y'=2\times3 - 3=3$, and $x'=-4$. So $D'(-4,3)$.

Step3: Find coordinates of $E$

The coordinates of $E$ are $(3,3)$. Using the formula $y'=2\times3 - 3 = 3$, and $x'=3$. So $E'(3,3)$.

Step4: Find coordinates of $F$

The coordinates of $F$ are $(4,8)$. Using the formula $y'=2\times3 - 8=- 2$, and $x'=4$. So $F'(4,-2)$.

Step5: Find coordinates of $G$

The coordinates of $G$ are $(-2,8)$. Using the formula $y'=2\times3 - 8=-2$, and $x'=-2$. So $G'(-2,-2)$.

Answer:

$D'(-4,3)$
$E'(3,3)$
$F'(4,-2)$
$G'(-2,-2)$