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: Recall the property of dilation

Dilation is a transformation that changes the size of a figure but not its shape. If a dilation maps one figure to another, the two figures are similar.

Step2: Check the center of dilation

For a dilation to map \(WXYZ\) to \(LMNO\), we need to check the center. If we consider the coordinates and the way the figure is scaled, we can see that the center of dilation should be a common point. By visual inspection of the grid - based figures (assuming proper coordinate - based analysis of side lengths and position relative to a center), we can see that the center is \(Y\).

Step3: Verify the scale factor

Let's assume we can calculate side lengths (using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) for corresponding sides of \(WXYZ\) and \(LMNO\)). If the ratio of the side lengths of \(LMNO\) to \(WXYZ\) is \(\frac{1}{3}\), then a dilation with scale factor \(\frac{1}{3}\) centered at \(Y\) maps \(WXYZ\) to \(LMNO\)

Answer:

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