Question

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△efg is a dilation of △efg with the center of dilation at the origin.
what is the scale factor of the dilation?
3/4 1/4 3 4

Explanation:

Step1: Find coordinates of corresponding points

Let's assume \(E(-4,4)\) and \(E'(-1,1)\) (by observing the graph).

Step2: Calculate the scale factor

The scale factor \(k\) for a dilation centered at the origin is given by \(k=\frac{x - coordinate\ of\ image}{x - coordinate\ of\ pre - image}\) (or \(\frac{y - coordinate\ of\ image}{y - coordinate\ of\ pre - image}\)). Using \(E\) and \(E'\), \(k=\frac{-1}{-4}=\frac{1}{4}\)

Answer:

\(\frac{1}{4}\)