Question

question
$\overline{uv}$ is dilated by a scale factor of 4 to form $\overline{uv}$. $\overline{uv}$ measures 56. what is the measure of $\overline{uv}$?
answer attempt 1 out of 2

Explanation:

Step1: Recall dilation formula

In dilation, the length of the image (\(U'V'\)) is equal to the scale factor (\(k\)) multiplied by the length of the original segment (\(UV\)). So the formula is \( U'V' = k \times UV \).

Step2: Substitute known values

We know \( U'V' = 56 \) and \( k = 4 \). Substituting into the formula gives \( 56 = 4 \times UV \).

Step3: Solve for \( UV \)

To find \( UV \), divide both sides of the equation by 4: \( UV=\frac{56}{4} = 14 \).

Answer:

14