graph the image of parallelogram cdef after a dilation with a scale factor of $\frac{1}{3}$, centered at the…

Explanation:

Step1: Identify the coordinates of the vertices of parallelogram CDEF

Assume (C(- 9,-9)), (D(-9,-6)), (E(9,9)), (F(9,6))

Step2: Apply the dilation formula for a dilation centered at the origin

The formula for a dilation centered at the origin with scale - factor (k) is ((x,y)\to(kx,ky)). Here (k = \frac{1}{3}). For point (C(-9,-9)): (\left(\frac{1}{3}\times(-9),\frac{1}{3}\times(-9)\right)=(-3,-3)) For point (D(-9,-6)): (\left(\frac{1}{3}\times(-9),\frac{1}{3}\times(-6)\right)=(-3,-2)) For point (E(9,9)): (\left(\frac{1}{3}\times9,\frac{1}{3}\times9\right)=(3,3)) For point (F(9,6)): (\left(\frac{1}{3}\times9,\frac{1}{3}\times6\right)=(3,2))

Step3: Plot the new points

Plot the points (C'(-3,-3)), (D'(-3,-2)), (E'(3,3)), (F'(3,2)) and connect them to form the dilated parallelogram.

Answer:

The new parallelogram has vertices (C'(-3,-3)), (D'(-3,-2)), (E'(3,3)), (F'(3,2)) and can be graphed on the coordinate - plane by plotting these points and connecting them in order.