Question

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

Explanation:

Step1: Recall rotation rule

When rotating a point \((x,y)\) \(270^{\circ}\) counter - clockwise about the origin, the rule is \((x,y)\to(y, - x)\).

Step2: Find coordinates of \(T\)

The coordinates of \(T\) are \((- 9,0)\). Using the rule \((x,y)\to(y, - x)\), we substitute \(x=-9\) and \(y = 0\). Then \(y = 0\) and \(-x=9\), so \(T'=(0,9)\).

Step3: Find coordinates of \(S\)

The coordinates of \(S\) are \((-9,-2)\). Using the rule \((x,y)\to(y, - x)\), we substitute \(x=-9\) and \(y=-2\). Then \(y=-2\) and \(-x = 9\), so \(S'=(-2,9)\).

Step4: Find coordinates of \(U\)

The coordinates of \(U\) are \((0,-3)\). Using the rule \((x,y)\to(y, - x)\), we substitute \(x = 0\) and \(y=-3\). Then \(y=-3\) and \(-x=0\), so \(U'=(-3,0)\).

Answer:

\(T'(0,9)\), \(S'(-2,9)\), \(U'(-3,0)\)