Question

1. triangle bcd is a dilated image of bcd. what is the measure of \\(\overline{bc}\\) if \\(\overline{bc} = 8\\) units and the scale factor is 4. show your work!!!

myerseducates, 2025.

Explanation:

Step1: Recall dilation formula

In dilation, the length of the image segment (\(B'C'\)) is equal to the scale factor (\(k\)) multiplied by the length of the original segment (\(BC\)). The formula is \( B'C' = k \times BC \).

Step2: Solve for \(BC\)

We know \( B'C' = 8 \) and \( k = 4 \). Rearranging the formula to solve for \(BC\), we get \( BC=\frac{B'C'}{k} \). Substituting the values, \( BC = \frac{8}{4} = 2 \).

Answer:

The measure of \(\overline{BC}\) is 2 units.