Question

1. quadrilateral abcd is shown on the coordinate grid below. what is the dilation factor that occurred? a. abcd was dilated by a scale factor of 0.25 b. abcd was dilated by a scale factor of -1 c. abcd was dilated by a scale factor of 0.5 d. abcd was dilated by a scale factor of 2

Explanation:

Step1: Observe corresponding side lengths

Let's take one side of the original quadrilateral \(ABCD\) and its corresponding side in the dilated - quadrilateral. For example, if we consider a horizontal or vertical side. Suppose we look at a side of the original quadrilateral that has a length of \(4\) units, and the corresponding side of the dilated quadrilateral has a length of \(2\) units.

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, \(k=\frac{\text{length of side of dilated figure}}{\text{length of side of original figure}}\). In our example, \(k = \frac{2}{4}=0.5\).

Answer:

b. \(ABCD\) was dilated by a scale factor of \(0.5\)