Question

the graph shows quadrilaterals qrst and vwxy. is qrst similar to vwxy? justify your answer. yes, because a dilation by a scale factor of 2 centered at the origin maps qrst onto vwxy. yes, because a dilation by a scale factor of 3 centered at the origin maps qrst onto vwxy. no, because $\frac{vw}{qr}$ is not equal to $\frac{xy}{st}$

Explanation:

Step1: Recall similarity condition

Two polygons are similar if the ratios of their corresponding - side lengths are equal.

Step2: Calculate side - length ratios

Let's assume we find the lengths of the sides of the quadrilaterals using the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). If the ratio of all corresponding sides of \(QRST\) and \(VWXY\) are the same, they are similar. If not, they are not similar. For two similar polygons, if we consider two corresponding sides \(a\) and \(b\) of the first polygon and \(c\) and \(d\) of the second polygon, \(\frac{a}{c}=\frac{b}{d}\). In the case of similar polygons formed by dilation, the ratio of corresponding side lengths is equal to the scale factor. Here, if we calculate the ratios of corresponding side lengths of \(QRST\) and \(VWXY\), we find that they are not equal. For example, if we calculate the lengths of \(VW\) and \(QR\) and \(XY\) and \(ST\) and find \(\frac{VW}{QR}
eq\frac{XY}{ST}\), the quadrilaterals are not similar.

Answer:

No, because \(\frac{VW}{QR}\) is not equal to \(\frac{XY}{ST}\)