write the coordinates of the vertices after a translation 10 units right and 6 units up.

Explanation:

Step1: Identify original coordinates

From the graph, the coordinates of point $B$ are $(- 5,-2)$ and of point $C$ are $(-5,1)$.

Step2: Apply translation rule

For a translation 10 units right and 6 units up, we add 10 to the $x$-coordinate and 6 to the $y$-coordinate. For point $B$: $x=-5 + 10=5$, $y=-2 + 6 = 4$. So $B'=(5,4)$. For point $C$: $x=-5+10 = 5$, $y=1 + 6=7$. So $C'=(5,7)$.

Answer:

$B'(5,4)$ $C'(5,7)$