Question

the triangle ( mno ) is a dilation of the triangle ( mno ). what is the scale factor of the dilation?
simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.

Explanation:

Step1: Find the length of a corresponding side in both triangles

In triangle \(MNO\), the length of \(OM\) (vertical side). The \(y -\)coordinate of \(M\) is \(10\) and of \(O\) is \(0\), so \(OM = 10\). In triangle \(M'N'O'\), the length of \(O'M'\). The \(y -\)coordinate of \(M'\) is \(8\) and of \(O'\) is \(0\), so \(O'M'=8\).

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the formula \(k=\frac{\text{length of side in image}}{\text{length of side in pre - image}}\). Here, \(k = \frac{O'M'}{OM}\). Substituting the values: \(k=\frac{8}{10}\).

Step3: Simplify the fraction

Simplify \(\frac{8}{10}\) by dividing both the numerator and the denominator by their greatest common divisor. The GCD of \(8\) and \(10\) is \(2\). So, \(\frac{8\div2}{10\div2}=\frac{4}{5}\).

Answer:

\(\frac{4}{5}\)