Question

the parallelogram ( jklm ) is a dilation of the parallelogram ( jklm ). 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 side of the original parallelogram

The length of side \(JK\) in parallelogram \(JKLM\): \(x\) - coordinate of \(J\) is \(- 2\), \(x\) - coordinate of \(K\) is \(8\). Using the distance formula for horizontal side \(d=\vert x_2 - x_1\vert\), \(JK=\vert8-(-2)\vert = 10\)

Step2: Find the length of the corresponding side of the dilated parallelogram

The length of side \(J'K'\) in parallelogram \(J'K'L'M'\): \(x\) - coordinate of \(J'\) is \(-1\), \(x\) - coordinate of \(K'\) is \(5\). Using the distance formula for horizontal side \(d = \vert x_2 - x_1\vert\), \(J'K'=\vert5-(-1)\vert=6\)

Step3: Calculate the scale factor

The scale factor \(k\) of a dilation is given by \(k=\frac{\text{length of side in image}}{\text{length of side in pre - image}}\). So \(k=\frac{J'K'}{JK}\)

Substitute \(J'K' = 6\) and \(JK = 10\) into the formula: \(k=\frac{6}{10}=\frac{3}{5}\)

Answer:

\(\frac{3}{5}\)