Question

1. write the coordinates of the vertices after a rotation 270° counterclockwise around the origin. graph the image and label.(4 pts)

Explanation:

Step1: Recall the rotation rule

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

Step2: Find the coordinates of \(T\)

The original coordinates of \(T\) is \((- 9,-1)\). Using the rule \((x,y)\to(y, - x)\), we substitute \(x=-9\) and \(y = - 1\). Then \(T'=(-1,9)\).

Step3: Find the coordinates of \(U\)

The original coordinates of \(U\) is \((-3,-1)\). Using the rule \((x,y)\to(y, - x)\), we substitute \(x = - 3\) and \(y=-1\). Then \(U'=(-1,3)\).

Step4: Find the coordinates of \(S\)

The original coordinates of \(S\) is \((-6,-5)\). Using the rule \((x,y)\to(y, - x)\), we substitute \(x=-6\) and \(y = - 5\). Then \(S'=(-5,6)\).

Step5: Find the coordinates of \(R\)

The original coordinates of \(R\) is \((-1,-5)\). Using the rule \((x,y)\to(y, - x)\), we substitute \(x=-1\) and \(y = - 5\). Then \(R'=(-5,1)\).

Answer:

\(T'(-1,9)\), \(U'(-1,3)\), \(S'(-5,6)\), \(R'(-5,1)\)