Question

1. graph the image after a rotation 270° counterclockwise around the origin. click to select polygon abcd

Explanation:

Step1: Find the coordinates of the original polygon

Assume the coordinates of \(A(-6,5)\), \(B(-3,5)\), \(C(-2,1)\), \(D(-7,1)\)

Step2: Apply the rotation rule

The rule for a \(270^{\circ}\) counter - clockwise rotation about the origin is \((x,y)\to(y, - x)\)
For point \(A(-6,5)\):
\(x=-6,y = 5\), after rotation \(A'=(5,6)\)
For point \(B(-3,5)\):
\(x=-3,y = 5\), after rotation \(B'=(5,3)\)
For point \(C(-2,1)\):
\(x=-2,y = 1\), after rotation \(C'=(1,2)\)
For point \(D(-7,1)\):
\(x=-7,y = 1\), after rotation \(D'=(1,7)\)

Step3: Plot the new points

Plot the points \(A'(5,6)\), \(B'(5,3)\), \(C'(1,2)\), \(D'(1,7)\) and connect them to form the polygon \(A'B'C'D'\)

Answer:

Plot the points \(A'(5,6)\), \(B'(5,3)\), \(C'(1,2)\), \(D'(1,7)\) and connect them.