Question

the parallelogram hijk is a dilation of the parallelogram hijk. 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 corresponding sides

For parallelogram \(HIJK\), let's find the length of side \(HI\). The \(x -\)coordinates of \(H(4, - 4)\) and \(I(4,1)\) (using the distance formula for vertical - side \(d=\vert y_2 - y_1\vert\)). So, \(HI=\vert1-(-4)\vert = 5\).
For parallelogram \(H'I'J'K'\), the \(x -\)coordinates of \(H'(7,-8)\) and \(I'(7,2)\) (using the distance formula for vertical - side \(d = \vert y_2 - y_1\vert\)). So, \(H'I'=\vert2-(-8)\vert=10\).

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by \(k=\frac{\text{length of side in image}}{\text{length of side in pre - image}}\).
Substitute the values: \(k=\frac{H'I'}{HI}\).
Since \(H'I' = 10\) and \(HI = 5\), then \(k=\frac{10}{5}=2\).

Answer:

\(2\)