Question

graph quadrilateral qrst and its image after a rotation 270° about the origin

Explanation:

Step1: Find the coordinates of the original quadrilateral QRST

From the graph, we can see that the coordinates of the vertices are \(Q(-7,-3)\), \(R(-6,0)\), \(S(-2,0)\), \(T(-1,-3)\)

Step2: Apply the rotation rule for a \(270^{\circ}\) rotation about the origin

The rule for a \(270^{\circ}\) rotation about the origin \((x,y)\to(y, -x)\)

• For point \(Q(-7,-3)\): After rotation, \(Q'(-3,7)\)
• For point \(R(-6,0)\): After rotation, \(R'(0,6)\)
• For point \(S(-2,0)\): After rotation, \(S'(0,2)\)
• For point \(T(-1,-3)\): After rotation, \(T'(-3,1)\)

Step3: Graph the original quadrilateral and its image

Plot the points \(Q(-7,-3)\), \(R(-6,0)\), \(S(-2,0)\), \(T(-1,-3)\) for the original quadrilateral QRST. Then plot the points \(Q'(-3,7)\), \(R'(0,6)\), \(S'(0,2)\), \(T'(-3,1)\) for the rotated quadrilateral \(Q'R'S'T'\)

Answer:

Graph the points \(Q(-7,-3)\), \(R(-6,0)\), \(S(-2,0)\), \(T(-1,-3)\) for quadrilateral QRST and \(Q'(-3,7)\), \(R'(0,6)\), \(S'(0,2)\), \(T'(-3,1)\) for its \(270^{\circ}\) - rotated image about the origin.