Question

quadrilateral jklm is dilated by a scale factor of $\frac{3}{4}$ to form quadrilateral jklm. what is the measure of side mj?

Explanation:

Step1: Recall dilation formula

If the scale - factor is $k$, and the length of a side in the original figure is $x$ and in the dilated figure is $y$, then $y = kx$. Here, we want to find the original side length $x$, and we know $y$ (length of side in dilated figure) and $k$ (scale - factor). Rearranging the formula gives $x=\frac{y}{k}$.

Step2: Identify values

The scale - factor $k = \frac{3}{4}$, and the length of side $M'J'$ in the dilated quadrilateral $J'K'L'M'$ is $y = 24$.

Step3: Calculate

Substitute the values into the formula $x=\frac{y}{k}=\frac{24}{\frac{3}{4}}=24\times\frac{4}{3}=32$.

Answer:

32