Question

d s: scale factor
grade math (illustrative math...
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son 3: more dilations
s: scale factor
s: scale factor
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grade math (illustrative math-

dilations, similarity, and

ng slope > more dilations
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triangle △abc is the image of
△abc under a dilation.
what is the scale factor of the
dilation?

Explanation:

Step1: Find the length of a side in the original triangle

Let's take side \(AB\). Counting the units on the grid, \(AB = 1\) unit.

Step2: Find the length of the corresponding side in the dilated triangle

The corresponding side \(A'B'\). Counting the units on the grid, \(A'B'= 3\) units.

Step3: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the formula \(k=\frac{\text{length of side in image}}{\text{length of side in original}}\). So \(k = \frac{A'B'}{AB}\). Substituting the values, \(k=\frac{3}{1}=3\).

Answer:

\(3\)