write the coordinates of the vertices after a rotation 270° counterclockwise around the origin.

Explanation:

Step1: Recall rotation rule

The rule for a 270 - counter - clockwise rotation around the origin is $(x,y)\to(y, - x)$.

Step2: Identify original coordinates

Let's assume the original coordinates of the vertices: $C(4,-8)$, $D(4,-4)$, $E(8,-4)$, $F(8,-8)$.

Step3: Apply rotation rule to $C$

For $C(4,-8)$, using the rule $(x,y)\to(y, - x)$, we get $C'(-8,-4)$.

Step4: Apply rotation rule to $D$

For $D(4,-4)$, using the rule $(x,y)\to(y, - x)$, we get $D'(-4,-4)$.

Step5: Apply rotation rule to $E$

For $E(8,-4)$, using the rule $(x,y)\to(y, - x)$, we get $E'(-4,-8)$.

Step6: Apply rotation rule to $F$

For $F(8,-8)$, using the rule $(x,y)\to(y, - x)$, we get $F'(-8,-8)$.

Answer:

$C'(-8,-4)$ $D'(-4,-4)$ $E'(-4,-8)$ $F'(-8,-8)$