Question

graph the image of \\( \triangle cde \\) after a rotation \\( 180^{\circ} \\) counterclockwise around the origin.

Explanation:

Step1: Find coordinates of original points

Assume \(C(2,2)\), \(D(4,2)\), \(E(5,1)\)

Step2: Apply rotation formula

The formula for a \(180^{\circ}\) counter - clockwise rotation around the origin is \((x,y)\to(-x,-y)\)
For point \(C(2,2)\): \((2,2)\to(- 2,-2)\)
For point \(D(4,2)\): \((4,2)\to(-4,-2)\)
For point \(E(5,1)\): \((5,1)\to(-5,-1)\)

Step3: Plot new points

Plot the points \(C'(-2,-2)\), \(D'(-4,-2)\), \(E'(-5,-1)\) and connect them to form \(\triangle C'D'E'\)

Answer:

Plot the points \(C'(-2,-2)\), \(D'(-4,-2)\), \(E'(-5,-1)\) and connect them.