Question

in the diagram, \\( \triangle l ^ { prime } m ^ { prime } n ^ { prime } \\) is the image of \\( \triangle l m n \\) under a dilation centered at the origin. what is the scale factor of the dilation?

Explanation:

Step1: Identify corresponding sides

In a dilation, the ratio of the length of a side in the image to the length of the corresponding side in the original figure gives the scale factor. Here, side \(NN'\) in the image and side \(NN\) (original) are corresponding. The length of \(NN'\) is \(31.5\) and the length of \(NN\) (original) is \(7\).

Step2: Calculate the scale factor

The formula for the scale factor \(k\) of a dilation is \(k=\frac{\text{length of side in image}}{\text{length of corresponding side in original}}\). So, \(k = \frac{31.5}{7}\)

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Answer:

The scale factor of the dilation is \(4.5\)