Question

the rectangle fghi is a dilation of the rectangle fghi. what is the scale factor of the dilation? simplify your answer and write it as a proper fraction, an improper fraction, or a whole

Explanation:

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

Let's consider the vertical side. In rectangle \(FGHI\), the length of the vertical side (e.g., from \(F\) to \(G\)) is \(10 - (- 10)=20\) units (using the \(y -\)coordinates: if \(F\) has \(y = 10\) and \(G\) has \(y=-10\)). In rectangle \(F'G'H'I'\), the length of the vertical side (e.g., from \(F'\) to \(G'\)) is \(2-(-2) = 4\) units (using the \(y -\)coordinates: \(F'\) has \(y = 2\) and \(G'\) has \(y=-2\)).

Step2: Calculate the scale factor

The formula for the scale factor \(k\) of a dilation is \(k=\frac{\text{length of side in image}}{\text{length of side in pre - image}}\). So \(k=\frac{4}{20}\). Simplifying \(\frac{4}{20}=\frac{4\div4}{20\div4}=\frac{1}{5}\).

Answer:

\(\frac{1}{5}\)