Question

quadrilateral m is a scaled copy of quadrilateral l. what scale factor takes quadrilateral l to quadrilateral m?

Explanation:

Step1: Recall scale - factor formula

The scale factor $k$ from a pre - image to an image is given by the ratio of corresponding side lengths. Let's take the ratio of the corresponding side lengths of the two quadrilaterals.

Step2: Calculate the scale factor

We can use either of the two given corresponding side lengths. Using the first pair of corresponding sides:
\[k=\frac{\text{Length in }M}{\text{Length in }L}\]
If we use the side lengths $\frac{1}{8}$ (in $M$) and $\frac{1}{10}$ (in $L$), then $k = \frac{\frac{1}{8}}{\frac{1}{10}}$.
When dividing by a fraction, we multiply by its reciprocal: $k=\frac{1}{8}\times\frac{10}{1}=\frac{10}{8}=\frac{5}{4}$.
We can also use the other pair of corresponding sides $\frac{3}{4}$ (in $M$) and $\frac{3}{5}$ (in $L$). Then $k=\frac{\frac{3}{4}}{\frac{3}{5}}$.
Since $\frac{\frac{3}{4}}{\frac{3}{5}}=\frac{3}{4}\times\frac{5}{3}=\frac{5}{4}$.

Answer:

$\frac{5}{4}$