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 - counter - clockwise rotation about the origin is $(x,y)\to(y, - x)$.

Step2: Identify original coordinates

From the graph, the coordinates of point $S$ are $(7,0)$, for point $T$ are $(7,6)$ and for point $U$ are $(1,1)$.

Step3: Apply rotation rule to point $S$

For $S(7,0)$, using the rule $(x,y)\to(y, - x)$, we get $(0,-7)$.

Step4: Apply rotation rule to point $T$

For $T(7,6)$, using the rule $(x,y)\to(y, - x)$, we get $(6,-7)$.

Step5: Apply rotation rule to point $U$

For $U(1,1)$, using the rule $(x,y)\to(y, - x)$, we get $(1,-1)$.

Answer:

$S(0,-7)$
$T(6,-7)$
$U(1,-1)$