Question

which of these statements is true about the two graphed parallelograms? a. they are similar, because one can be obtained by dilating the other about the origin with a scale factor of 1/4. b. they are similar, because one can be obtained by dilating the other about the origin with a scale factor of 1/2. c. they are not similar, because one can be obtained by dilating the other about the origin with a scale factor of 1/4. d. they are not similar, because one can be obtained by dilating the other about the origin with a scale factor of 1/2.

Explanation:

Step1: Recall similarity of figures

Two figures are similar if one can be obtained from the other by dilation (scaling) about a point (in this case the origin). The corresponding sides of similar figures are in proportion.

Step2: Analyze the given parallelograms

By observing the parallelograms on the coordinate - grid, we can see that the larger parallelogram can be dilated to get the smaller parallelogram about the origin. If we consider the lengths of the corresponding sides, we find that the scale factor from the larger to the smaller parallelogram is $\frac{1}{2}$.

Answer:

B. They are similar, because one can be obtained by dilating the other about the origin with a scale factor of $\frac{1}{2}$.