Question

identify the center and scale factor of the dilation that maps figure ( abcd ) onto figure ( fghi ).
the center of dilation is point (square).
the scale factor is (square).

Explanation:

Step1: Determine the center of dilation

The center of dilation is the fixed point about which the figure is dilated. By observing the figure, we can see that point \(C\) is the center of dilation.

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is the ratio of the length of a corresponding side of the image to the length of the side of the original figure.
We know that a side of the original figure \(ABCD\) (e.g., \(CB = 2.5\)) and the corresponding side of the image \(FGHI\) (e.g., \(CG=10\)).
The scale factor \(k=\frac{CG}{CB}\)
Substitute \(CG = 10\) and \(CB=2.5\) into the formula: \(k=\frac{10}{2.5}=4\)

Answer:

The center of dilation is point \(C\).
The scale factor is \(4\).