Question

question
triangle wxy is dilated by a scale factor of $\frac{1}{3}$ to form triangle wxy. side yw measures 7.
what is the measure of side yw?

Explanation:

Step1: Recall dilation formula

The length of a side in the dilated - figure ($l_{d}$) is related to the length of the corresponding side in the original figure ($l_{o}$) by the formula $l_{d}=k\times l_{o}$, where $k$ is the scale factor. Here, $l_{d} = Y'W'$, $k=\frac{1}{3}$, and $l_{o}=YW$.

Step2: Rearrange the formula to solve for $YW$

We can rewrite the formula as $YW=\frac{Y'W'}{k}$.

Step3: Substitute the given values

Given $Y'W' = 7$ and $k=\frac{1}{3}$, we substitute these values into the formula: $YW=\frac{7}{\frac{1}{3}}$.

Step4: Calculate the value of $YW$

When dividing by a fraction, we multiply by its reciprocal. So, $YW = 7\times3=21$.

Answer:

21