Question

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

Explanation:

Step1: Recall Dilation Rule

Dilation with scale factor \( k \) means the image length is \( k \times \) original length. Here, scale factor \( k=\frac{5}{4} \), original length \( CA = 8 \).

Step2: Calculate \( C'A' \)

Multiply \( CA \) by scale factor: \( C'A'=\frac{5}{4}\times CA \). Substitute \( CA = 8 \): \( C'A'=\frac{5}{4}\times8 = 5\times2 = 10 \)? Wait, no, wait—wait, maybe I mixed up? Wait, no, dilation rule \( D_{Y,\frac{5}{4}} \) means the scale factor is \( \frac{5}{4} \), so image length is scale factor times original. Wait, but wait, maybe I miscalculated. Wait, \( \frac{5}{4} \times 8 = 10 \)? But the options have 10 as first option. Wait, but let me check again. \( 8 \times \frac{5}{4} = (8\div4)\times5 = 2\times5 = 10 \). Yes.

Answer:

10 units (the first option: 10 units)