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

Explanation:

Step1: Recall reflection rule

When reflecting a point $(x,y)$ over the line $y = x$, the coordinates swap, becoming $(y,x)$.

Step2: Find coordinates of B

The coordinates of point B are $(- 6,0)$. After reflection over $y = x$, the new - coordinates $B'$ are $(0,-6)$.

Step3: Find coordinates of C

The coordinates of point C are $(-6,8)$. After reflection over $y = x$, the new - coordinates $C'$ are $(8,-6)$.

Step4: Find coordinates of D

The coordinates of point D are $(-4,8)$. After reflection over $y = x$, the new - coordinates $D'$ are $(8,-4)$.

Step5: Find coordinates of E

The coordinates of point E are $(-4,0)$. After reflection over $y = x$, the new - coordinates $E'$ are $(0,-4)$.

Answer:

$B'(0,-6)$ $C'(8,-6)$ $D'(8,-4)$ $E'(0,-4)$