Question

write the coordinates of the vertices after a rotation 180° clockwise around the origin.

Explanation:

Step1: Identify original coordinates

The original coordinates of point $D$ are $(-5,2)$, of point $E$ are $(-2,2)$ and of point $F$ are $(-2,9)$.

Step2: Apply rotation rule

The rule for a $180^{\circ}$ clock - wise rotation around the origin is $(x,y)\to(-x,-y)$.
For point $D(-5,2)$:
$x=-5,y = 2$, after rotation $x'=-(-5)=5,y'=-2$. So $D'=(5,-2)$.
For point $E(-2,2)$:
$x=-2,y = 2$, after rotation $x'=-(-2)=2,y'=-2$. So $E'=(2,-2)$.
For point $F(-2,9)$:
$x=-2,y = 9$, after rotation $x'=-(-2)=2,y'=-9$. So $F'=(2,-9)$.

Answer:

$D'(5,-2),E'(2,-2),F'(2,-9)$