Question

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

Explanation:

Step1: Recall the formula for scale factor

The scale factor \(k\) from the original figure (quadrilateral \(L\)) to the scaled - copy (quadrilateral \(M\)) is given by \(k=\frac{\text{length of a side in }M}{\text{length of the corresponding side in }L}\).

Step2: Identify corresponding sides

We can use either of the two given side - pairs. Let's use the side of length \(18\) in \(L\) and the corresponding side of length \(9\) in \(M\), or the side of length \(36\) in \(L\) and the corresponding side of length \(18\) in \(M\).
Using the first pair: \(k = \frac{9}{18}\).
Using the second pair: \(k=\frac{18}{36}\).

Step3: Simplify the fraction

For \(k = \frac{9}{18}\), we can factor out a \(9\) from the numerator and the denominator. \(\frac{9\div9}{18\div9}=\frac{1}{2}\).
For \(k=\frac{18}{36}\), we can factor out an \(18\) from the numerator and the denominator. \(\frac{18\div18}{36\div18}=\frac{1}{2}\).

Answer:

\(\frac{1}{2}\)