Question

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 12. is the dilation an enlargement or a reduction? reduction ○ enlargement ● the scale factor of the dilation is \\(\frac{4}{3}\\). (simplify your answer.)

Explanation:

Step1: Identify original/image side lengths

Original side $AB = 9$, image side $AC = 12$

Step2: Calculate scale factor

Scale factor = $\frac{\text{Image length}}{\text{Original length}} = \frac{AC}{AB} = \frac{12}{9} = \frac{4}{3}$

Step3: Classify dilation type

Since $\frac{4}{3} > 1$, it is an enlargement.

Answer:

1. The dilation is an enlargement.
2. The scale factor of the dilation is $\frac{4}{3}$