Question

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

Explanation:

Step1: Find side - length of original and dilated rectangles

Let's consider the vertical side of the rectangles. For rectangle \(JKLM\), if we consider the \(y\) - coordinates of \(K(0,10)\) and \(J(0, - 10)\), the length of the vertical side \(KJ=10-( - 10)=20\). For rectangle \(J'K'L'M'\), if we consider the \(y\) - coordinates of \(K'(0,2)\) and \(J'(0, - 2)\), the length of the vertical side \(K'J'=2-( - 2)=4\).

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by the ratio of the length of a side of the dilated figure to the length of the corresponding side of the original figure. So, \(k=\frac{K'J'}{KJ}\). Substituting the values we found: \(k = \frac{4}{20}=\frac{1}{5}\).

Answer:

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