Question

help me solve this view an example get more help. the triangle ace, is a dilation image of triangle abd. point a is the center of dilation. tell whether the dilation is an enlargement or a reduction. then find the scale factor of the dilation. the length of side ac is 15. is the dilation an enlargement or a reduction? o enlargement o reduction clear all

Explanation:

Step1: Determine if it is an enlargement or reduction

Since \(AC = 15\) and \(AB=9\), and \(15>9\), the image (triangle \(ACE\)) is larger than the pre - image (triangle \(ABD\)). So it is an enlargement.

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the formula \(k=\frac{\text{length of a side of the image}}{\text{length of the corresponding side of the pre - image}}\).
Here, the corresponding sides are \(AC\) (image) and \(AB\) (pre - image). So \(k = \frac{AC}{AB}\).
Substitute \(AC = 15\) and \(AB = 9\) into the formula: \(k=\frac{15}{9}=\frac{5}{3}\)

Answer:

Enlargement, scale factor \(\frac{5}{3}\)