Question

write the coordinates of the vertices after a translation 5 units right and 8 units up.
d( , )
e( , )
f( , )
g( , )

Explanation:

Step1: Identify original coordinates

Original vertices: $D(-8, -4)$, $E(-8, -2)$, $F(-7, -2)$, $G(-7, -4)$

Step2: Apply translation rule

For a point $(x,y)$, translate right 5, up 8: $(x+5, y+8)$

Step3: Calculate $D'$

$$\begin{aligned} x &= -8 + 5 = -3 \\ y &= -4 + 8 = 4 \end{aligned}$$

Step4: Calculate $E'$

$$\begin{aligned} x &= -8 + 5 = -3 \\ y &= -2 + 8 = 6 \end{aligned}$$

Step5: Calculate $F'$

$$\begin{aligned} x &= -7 + 5 = -2 \\ y &= -2 + 8 = 6 \end{aligned}$$

Step6: Calculate $G'$

$$\begin{aligned} x &= -7 + 5 = -2 \\ y &= -4 + 8 = 4 \end{aligned}$$

Answer:

$D'(-3, 4)$
$E'(-3, 6)$
$F'(-2, 6)$
$G'(-2, 4)$