Question

rectangle efgh was dilated with the origin as the center of dilation to create rectangle efgh.
what scale factor was applied to rectangle efgh to create rectangle efgh?

Explanation:

Step1: Find coordinates of corresponding points

Let's take point \(F\) and \(F'\). Suppose \(F(-1,4)\) and \(F'(-1,2)\) (assuming each grid unit is \(1\)).

Step2: Calculate the scale factor

The scale factor \(k\) for dilation about the origin is given by \(k=\frac{y - coordinate\ of\ image}{y - coordinate\ of\ pre - image}\) (or \(k = \frac{x - coordinate\ of\ image}{x - coordinate\ of\ pre - image}\) for horizontal dilation, but since it's a rectangle, we can use vertical or horizontal). Using \(y\) - coordinates: \(k=\frac{2}{4}=\frac{1}{2}\)

Answer:

\(\frac{1}{2}\)