Question

write the coordinates of the vertices after a translation 3 units left and 5 units down.

Explanation:

Step1: Identify original coordinates

The original coordinates are $D(0, - 3)$, $E(0,4)$, $F(8,4)$, $G(8,-3)$.

Step2: Apply left - translation rule

For a translation 3 units left, subtract 3 from the x - coordinate of each point.
$D(0, - 3)\to D_1(-3,-3)$, $E(0,4)\to E_1(-3,4)$, $F(8,4)\to F_1(5,4)$, $G(8,-3)\to G_1(5,-3)$.

Step3: Apply down - translation rule

For a translation 5 units down, subtract 5 from the y - coordinate of each point.
$D_1(-3,-3)\to D'(-3,-8)$, $E_1(-3,4)\to E'(-3,-1)$, $F_1(5,4)\to F'(5,-1)$, $G_1(5,-3)\to G'(5,-8)$.

Answer:

$D'(-3,-8)$
$E'(-3,-1)$
$F'(5,-1)$
$G'(5,-8)$