Question

triangle abc is dilated to create triangle abc using point o as the center of dilation. what is the scale factor of the dilation? 1/3 3 4 1/4

Explanation:

Step1: Recall the formula for scale factor

The scale factor \(k\) of a dilation with center \(O\) is given by \(k=\frac{\text{length of segment from }O\text{ to image point}}{\text{length of segment from }O\text{ to original point}}\).

Step2: Identify the lengths

We have \(OA = 3\) and \(OA'=3 + 9=12\). Using the formula \(k=\frac{OA'}{OA}\).

Step3: Calculate the scale factor

Substitute the values: \(k=\frac{12}{3}=4\).

Answer:

\(4\)