Question

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

Explanation:

Step1: Recall rotation rule

The rule for a 180 - degree clockwise rotation around the origin is $(x,y)\to(-x,-y)$.

Step2: Find coordinates of point R

Assume the coordinates of point R are $(-5,2)$. After rotation, the new coordinates are $R'(5, - 2)$ since $x=-5,y = 2$ and $-x = 5,-y=-2$.

Step3: Find coordinates of point U

If the coordinates of point U are $(-4,2)$, after rotation, the new coordinates are $U'(4,-2)$ as $x=-4,y = 2$ and $-x = 4,-y=-2$.

Step4: Find coordinates of point T

Suppose the coordinates of point T are $(-4,9)$. After rotation, the new coordinates are $T'(4,-9)$ because $x=-4,y = 9$ and $-x = 4,-y=-9$.

Step5: Find coordinates of point S

If the coordinates of point S are $(-5,9)$, after rotation, the new coordinates are $S'(5,-9)$ since $x=-5,y = 9$ and $-x = 5,-y=-9$.

Answer:

$R'(5, - 2),U'(4,-2),T'(4,-9),S'(5,-9)$