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 \(k=\frac{OA'}{OA}\) (where \(OA'\) is the distance from the center of dilation to a point on the image and \(OA\) is the distance from the center of dilation to the corresponding point on the pre - image).

Step2: Identify the values of \(OA'\) and \(OA\)

From the figure, \(OA = 3\) and \(OA'=9\).

Step3: Calculate the scale factor

Substitute the values into the formula: \(k=\frac{OA'}{OA}=\frac{9}{3}=3\)

Answer:

3