Question

1. triangle abc is a dilated image of triangle abc. what is the measure of \\(\overline{ab}\\) if \\(\overline{ab} = 12\\) and the scale factor is \\(\frac{1}{3}\\). show your work!!!

Explanation:

Step1: Recall dilation formula

In dilation, the length of a side of the dilated figure is the length of the corresponding side of the original figure multiplied by the scale factor. So, \( A'B' = AB \times \text{scale factor} \).

Step2: Substitute values

Given \( AB = 12 \) and scale factor \( = \frac{1}{3} \), substitute into the formula: \( A'B' = 12 \times \frac{1}{3} \).

Step3: Calculate the product

\( 12 \times \frac{1}{3} = \frac{12}{3} = 4 \).

Answer:

The measure of \( \overline{A'B'} \) is 4.