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 the dilation formula

When a figure is dilated with a scale factor \(k\), the length of a segment \(AB\) in the original figure and the length of its image \(A'B'\) in the dilated figure are related by the formula \(A'B'=k\times AB\). Here, the scale factor \(k = \frac{5}{4}\) and \(CA = 8\).

Step2: Calculate \(C'A'\)

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

$$ \frac{5}{4}\times8=\frac{5\times8}{4}=5\times2 = 10 $$

Answer:

10 units