Question

1. (3 - 29) rakisha is puzzled. she is working with the parallelogram drawn at right and wants to make it smaller instead of bigger. a. what should she do if she wants the sides of her new figure to be half as long as the original sides? what zoom factor should she use? find the dimensions of her new figure. b. while drawing some other shapes, rakisha ended up with a shape congruent to the original parallelogram. what is the common ratio between pairs of corresponding sides?

Explanation:

Step1: Determine the scale - factor for making the figure half as long

To make the new figure half as long as the original, we use a scale - factor. The scale - factor $k$ is related to the ratio of the new length to the original length. If the new length is half of the original length, the scale - factor $k=\frac{1}{2}$.

Step2: Recall the property of similar shapes for the ratio of corresponding sides

For two similar shapes (in this case, the original and the new parallelogram), the ratio of the lengths of corresponding sides is equal to the scale - factor. Since the new parallelogram is similar to the original one and we used a scale - factor of $\frac{1}{2}$ to create it, the ratio of the lengths of corresponding sides of the new parallelogram to the original parallelogram is $\frac{1}{2}$.

Answer:

a. The zoom factor she should use is $\frac{1}{2}$.
b. The ratio between the pairs of corresponding sides of the new shape to the original shape is $\frac{1}{2}$.