Question

triangle abc is dilated to form triangle xyz. find the scale factor by writing the quotients of the corresponding side lengths as fractions. the scale factor is □. = 12/16 = □ use the number pad to enter your answers in the boxes.

Explanation:

Step1: Find the ratio of corresponding sides

We can use the ratio of side \(BC\) to \(YZ\) (or \(AB\) to \(XY\) or \(AC\) to \(XZ\)). Let's use \(BC = 12\) cm and \(YZ=9\) cm. The ratio is \(\frac{YZ}{BC}\) (since we are going from \(\triangle ABC\) to \(\triangle XYZ\)).
\(\frac{9}{12}=\frac{3}{4}\)
We can also check with another pair of sides. Let's take \(AB = 20\) cm and \(XY = 15\) cm. \(\frac{XY}{AB}=\frac{15}{20}=\frac{3}{4}\)
Another pair: \(AC = 16\) cm and \(XZ = 12\) cm. \(\frac{XZ}{AC}=\frac{12}{16}=\frac{3}{4}\)

Answer:

\(\frac{3}{4}\)