Question

a dilation of triangle gef using:

center of dilation: point e scale factor: 2

center of dilation: point e scale factor: 1/2

center of dilation: point g scale factor: 2

center of dilation: point g scale factor: 1/2

Explanation:

Step1: Recall the dilation formula

The formula for dilation is \(d = k\times o\), where \(d\) is the distance of the dilated point from the center, \(k\) is the scale factor, and \(o\) is the original distance from the center.

Step2: Analyze the given lengths

We have \(GG'= 4\) units and \(GF = 8\) units. Let's assume the center of dilation is \(E\).
The scale factor \(k=\frac{GG'}{GF}\) (if we consider the ratio of the lengths from the center of dilation). Since \(GG' = 4\) and \(GF=8\), the scale factor \(k=\frac{4}{8}=\frac{1}{2}\) is incorrect. Wait, no, actually, if we consider the dilation of \(\triangle GEF\) to \(\triangle G'EF'\). The length \(GG'\) and \(GF\) are related. If we assume the center of dilation is \(E\), and we know that for a dilation, if a point \(P\) is dilated to \(P'\) with center \(C\), then \(\frac{CP'}{CP}=k\). Here, if we consider the line segments \(EG\) and \(EG'\). But looking at the figure, we can see that the scale factor \(k = \frac{1}{2}\) (since \(4=\frac{1}{2}\times8\)) and the center of dilation is \(E\) (because the lines \(GG'\) and \(FF'\) (implied by the dilation) intersect at \(E\)).

Answer:

C. Center of dilation: Point E Scale Factor: \(1/2\)