Question

write the coordinates of the vertices after a translation 5 units right and 1 unit up.

Explanation:

Step1: Identify original coordinates

The original coordinates are: $R(-2,-8)$, $S(4,-8)$, $T(4,0)$, $U(-2,0)$.

Step2: Apply translation rule

For a translation 5 units right and 1 unit up, we add 5 to the x - coordinate and 1 to the y - coordinate of each point.
For point $R$: $x=-2 + 5=3$, $y=-8 + 1=-7$, so $R'(3,-7)$.
For point $S$: $x=4 + 5=9$, $y=-8 + 1=-7$, so $S'(9,-7)$.
For point $T$: $x=4 + 5=9$, $y=0 + 1=1$, so $T'(9,1)$.
For point $U$: $x=-2 + 5=3$, $y=0 + 1=1$, so $U'(3,1)$.

Answer:

$R'(3,-7)$
$S'(9,-7)$
$T'(9,1)$
$U'(3,1)$