Question

the parallelogram ( ijkl ) is a dilation of the parallelogram ( ijkl ). 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

Let's consider side \(IJ\) and \(I'J'\).
The length of \(IJ\): \(I(10,-5)\), \(J(-6,-5)\). Using the distance formula for horizontal line (since \(y -\)coordinates are same), \(d=\vert x_2 - x_1\vert\). So \(IJ=\vert10-(-6)\vert = 16\).
The length of \(I'J'\): \(I'(6,-3)\), \(J'(-2,-3)\). Using the distance formula for horizontal line (since \(y -\)coordinates are same), \(d=\vert x_2 - x_1\vert\). So \(I'J'=\vert6-(-2)\vert = 8\).

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by \(k=\frac{\text{length of image}}{\text{length of pre - image}}\).
So \(k=\frac{I'J'}{IJ}\). Substituting the values: \(k = \frac{8}{16}\).

Answer:

\(\frac{1}{2}\)