Question

triangle abc was dilated using the rule ( d_{y,\frac{5}{4}} ). if ( ca = 8 ), what is ( ca )? 10 units 12 units 16 units 20 units

Explanation:

Step1: Recall dilation formula

When a figure is dilated with a scale factor \(k\), the length of a segment \(s'\) in the dilated figure is \(s'=k\times s\), where \(s\) is the length of the corresponding segment in the original figure. Here, the scale factor \(k = \frac{5}{4}\) and \(s = CA=8\).

Step2: Calculate \(C'A'\)

Substitute \(k=\frac{5}{4}\) and \(s = 8\) into the formula \(C'A'=k\times CA\). So \(C'A'=\frac{5}{4}\times8\).

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Answer:

10 units