Question

triangle abc was dilated using the rule $d_{y, \frac{1}{4}}$. if $ca = 8$, what is $ca$? 12 units 10 units 16 units 20 units

Explanation:

Step1: Identify Dilation Scale Factor

From the diagram, observe that the dilation rule is \( D_{Y,\frac{1}{2}} \)? Wait, no, looking at the segments, \( YA' \) seems to be twice \( YA \), and \( YB' \) twice \( YB \), so the scale factor \( k = 2 \).

Step2: Apply Dilation to Segment \( CA \)

Dilation scales lengths by the scale factor. So \( C'A' = k \times CA \). Given \( CA = 8 \), \( k = 2 \), so \( C'A' = 2 \times 8 = 16 \).

Answer:

16 units