Question

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

Explanation:

Step1: Recall translation rule

For a translation 5 units right and 1 unit up, the rule for a point $(x,y)$ is $(x + 5,y+1)$.

Step2: Find coordinates of point R

The original coordinates of $R$ are $(-2,-8)$. Applying the rule: $x=-2,y = - 8$, so the new $x$-coordinate is $-2 + 5=3$, and the new $y$-coordinate is $-8 + 1=-7$. So $R'=(3,-7)$.

Step3: Find coordinates of point S

The original coordinates of $S$ are $(4,-8)$. Applying the rule: new $x$-coordinate is $4 + 5=9$, new $y$-coordinate is $-8 + 1=-7$. So $S'=(9,-7)$.

Step4: Find coordinates of point T

The original coordinates of $T$ are $(4,-1)$. Applying the rule: new $x$-coordinate is $4+5 = 9$, new $y$-coordinate is $-1 + 1=0$. So $T'=(9,0)$.

Step5: Find coordinates of point U

The original coordinates of $U$ are $(-2,-1)$. Applying the rule: new $x$-coordinate is $-2+5 = 3$, new $y$-coordinate is $-1 + 1=0$. So $U'=(3,0)$.

Answer:

$R'(3,-7),S'(9,-7),T'(9,0),U'(3,0)$