Question

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

Explanation:

Step1: Recall rotation rule

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

Step2: Identify original coordinates

From the graph, the coordinates of the vertices are $C(4,-8)$, $D(4,-4)$, $E(6,-4)$, $F(6,-8)$.

Step3: Apply rotation rule to point C

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

Step4: Apply rotation rule to point D

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

Step5: Apply rotation rule to point E

For $E(6,-4)$, using the rule $(x,y)\to(y, - x)$, we get $E'(-4,-6)$.

Step6: Apply rotation rule to point F

For $F(6,-8)$, using the rule $(x,y)\to(y, - x)$, we get $F'(-8,-6)$.

Answer:

$C'(-8,-4)$
$D'(-4,-4)$
$E'(-4,-6)$
$F'(-8,-6)$