Question

in each part, dilate the solid figure exactly onto the dashed figure. if this is not possible, click on
ot possible\. (note that the dilations are centered at the origin.)

Explanation:

Step1: Recall dilation property

Dilation centered at the origin multiplies the coordinates of each point of a figure by a scale - factor. For two similar figures related by dilation centered at the origin, the ratio of corresponding side - lengths is constant.

Step2: Analyze first pair of figures

In the first pair of figures, the solid and dashed rectangles are similar and the dilation is possible. We can find a scale - factor. Let's assume the side - lengths of the solid rectangle are \(a\) and \(b\), and of the dashed rectangle are \(ka\) and \(kb\) where \(k\) is the scale - factor.

Step3: Analyze second pair of figures

In the second pair of figures, the solid and the dashed figures are not similar in the way required for a dilation centered at the origin. The shapes do not have a constant ratio of corresponding side - lengths. So dilation is not possible.

Answer:

First part: Possible
Second part: Not possible