Question

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

Explanation:

Step1: Find coordinates of original points

Assume coordinates from graph: \(C(-3,-2)\), \(D(-3, - 0)\) (assuming \(D\) is at \((-3,0)\) as per grid), \(E(-9,-1)\)

Step2: Apply rotation formula

The formula for a \(180^{\circ}\) counter - clockwise rotation about the origin is \((x,y)\to(-x,-y)\)
For \(C(-3,-2)\): \((-(-3),-(-2))=(3,2)\)
For \(D(-3,0)\): \((-(-3),-0)=(3,0)\)
For \(E(-9,-1)\): \((-(-9),-(-1))=(9,1)\)

Step3: Plot new points

Plot \(C'(3,2)\), \(D'(3,0)\), \(E'(9,1)\) and connect them to form \(\triangle C'D'E'\)

Answer:

Plot the points \((3,2)\), \((3,0)\), \((9,1)\) and connect them to get the image of \(\triangle CDE\) after \(180^{\circ}\) rotation about the origin.