Question

question
$overline{op}$ is dilated by a scale factor of $\frac{3}{4}$ to form $overline{op}$. $overline{op}$ measures 22. what is the measure of $overline{op}$?
answer
attempt 1 out of 2

Explanation:

Step1: Recall dilation formula

The length of the dilated segment $O'P'$ is the product of the scale - factor and the length of the original segment $OP$. Let the scale - factor be $k$ and the length of $OP$ be $l_{OP}$, and the length of $O'P'$ be $l_{O'P'}$. Then $l_{O'P'}=k\times l_{OP}$.

Step2: Substitute values

We are given that $k = \frac{3}{4}$ and $l_{OP}=22$. So $l_{O'P'}=\frac{3}{4}\times22$.
$l_{O'P'}=\frac{3\times22}{4}=\frac{66}{4} = 16.5$.

Answer:

$16.5$