Question

draw the image of the rotation of quadrilateral sort by 270° about the origin.

Explanation:

Step1: Recall rotation rule

When rotating a point \((x,y)\) by \(270^{\circ}\) about the origin, the new coordinates \((x',y')\) are given by the rule \((x,y)\to(y, -x)\).

Step2: Find coordinates of each vertex

• For \(S(-2,2)\): Using the rule \((x,y)\to(y, -x)\), we get \(S'(2,2)\).
• For \(O(-2,-1)\): Using the rule \((x,y)\to(y, -x)\), we get \(O'(-1,2)\).
• For \(R(-2,3)\): Using the rule \((x,y)\to(y, -x)\), we get \(R'(3,2)\).
• For \(T(6,-6)\): Using the rule \((x,y)\to(y, -x)\), we get \(T'(-6,6)\).

Step3: Plot the new points

Plot the points \(S'(2,2)\), \(O'(-1,2)\), \(R'(3,2)\) and \(T'(-6,6)\) on the coordinate plane and connect them to form the rotated quadrilateral.

Answer:

Follow the above steps to draw the rotated quadrilateral on the coordinate - plane.