Question

the pink figure is a dilation image of the black figure. the labeled point is the center of dilation. tell whether the dilation is an enlargement or a reduction. then find the scale factor of the dilation.
is the dilation an enlargement or a reduction?
reduction
enlargement
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Explanation:

Step1: Determine if it's an enlargement or reduction

Since the pink figure is smaller than the black figure, it is a reduction.

Step2: Calculate the scale factor

Let's assume a side - length of the black figure is \(4\) units (for example, if we count the number of dots between two vertices) and the corresponding side - length of the pink figure is \(2\) units. The scale factor \(k\) of a dilation is given by the formula \(k=\frac{\text{length of image}}{\text{length of pre - image}}\). So, \(k = \frac{2}{4}=\frac{1}{2}\)

Answer:

Reduction, scale factor \(\frac{1}{2}\)