Question

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

Explanation:

Step1: Find the coordinates of the original parallelogram

Assume the coordinates of \(C(-9,-9)\), \(D(-9,-6)\), \(E(9,9)\), \(F(9,6)\) (by observing the graph).

Step2: Apply the dilation formula

The dilation formula centered at the origin is \((x,y)\to(\frac{1}{3}x,\frac{1}{3}y)\).
For point \(C(-9,-9)\): \((\frac{1}{3}\times(-9),\frac{1}{3}\times(-9))=(-3,-3)\)
For point \(D(-9,-6)\): \((\frac{1}{3}\times(-9),\frac{1}{3}\times(-6))=(-3,-2)\)
For point \(E(9,9)\): \((\frac{1}{3}\times9,\frac{1}{3}\times9)=(3,3)\)
For point \(F(9,6)\): \((\frac{1}{3}\times9,\frac{1}{3}\times6)=(3,2)\)

Answer:

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