Question

is wxyz similar to lmno? justify your answer.
yes, because a dilation by a scale factor of \\( \frac { 1 } { 3 } \\) centered at point w maps wxyz onto lmno.
yes, because a dilation by a scale factor of \\( \frac { 1 } { 3 } \\) centered at point y maps wxyz onto lmno.

Explanation:

Step1: Analyze the scale factor

To check similarity via dilation, we need to find the ratio of corresponding side lengths. Let's assume we can calculate the lengths of \(MN\) and \(XY\) (or other corresponding sides). If the scale factor is consistent for all corresponding sides.

Step2: Check the center of dilation

If we consider the coordinates of the points. For a dilation, the center of dilation is a fixed point. If we assume we calculate the distances from the center of dilation to the corresponding points of the two figures. For example, if we take point \(Y\) as the center of dilation. Let's assume the coordinates of \(M\) and \(W\), \(N\) and \(X\) (adjusting for the center \(Y\)).

Answer:

The second option: Yes, because a dilation by a scale factor of \(\frac{1}{3}\) centered at point \(Y\) maps \(WXYZ\) onto \(LMNO\).