Question

calculating a scale factor
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
1/4
3
4

Explanation:

Step1: Recall the scale - factor formula

The scale factor \(k\) of a dilation with center \(O\) is given by \(k=\frac{\text{distance from }O\text{ to a point on the image}}{\text{distance from }O\text{ to the corresponding point on the pre - image}}\).

Step2: Identify the distances

We know that \(OA = 3\) (distance from center \(O\) to a point \(A\) on the pre - image \(\triangle ABC\)) and \(OA'=3 + 9=12\) (distance from center \(O\) to the corresponding point \(A'\) on the image \(\triangle A'B'C'\)).

Step3: Calculate the scale factor

Using the formula \(k=\frac{OA}{OA'}\), we substitute the values: \(k=\frac{3}{12}=\frac{1}{4}\).

Answer:

\(\frac{1}{4}\)