Question

graph the image of △efg after a dilation with a scale factor of 1/3, centered at the origin.

Explanation:

Step1: Identify coordinates of vertices

Let's assume $E(-6,9)$, $F(7,9)$, $G(-6,-9)$ by observing the graph.

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor $k = \frac{1}{3}$, if a point $(x,y)$ is dilated, the new point $(x',y')$ is given by $(x',y')=(k x,k y)$.
For point $E(-6,9)$:
$x_E'=\frac{1}{3}\times(-6)= - 2$
$y_E'=\frac{1}{3}\times9 = 3$
So $E'(-2,3)$.
For point $F(7,9)$:
$x_F'=\frac{1}{3}\times7=\frac{7}{3}$
$y_F'=\frac{1}{3}\times9 = 3$
So $F'(\frac{7}{3},3)$.
For point $G(-6,-9)$:
$x_G'=\frac{1}{3}\times(-6)=-2$
$y_G'=\frac{1}{3}\times(-9)= - 3$
So $G'(-2,-3)$.

Step3: Plot new points

Plot the points $E'(-2,3)$, $F'(\frac{7}{3},3)$, $G'(-2,-3)$ on the coordinate - plane and connect them to form the dilated triangle $\triangle E'F'G'$.

Answer:

Plot points $E'(-2,3)$, $F'(\frac{7}{3},3)$, $G'(-2,-3)$ and connect them.