Question

triangle abc was dilated by 50%. what is the relationship between ac and ac? a ac = ac b ac = 5(ac) c ac = \frac{1}{2}(ac) d \frac{1}{2}(ac) = ac e \frac{1}{4}(ac) = ac

Explanation:

Step1: Understand Dilation Scale Factor

Dilation by 50% means the scale factor \( k = 0.5=\frac{1}{2} \). For a dilation, the length of the image ( \( A'C' \)) is the original length ( \( AC \)) multiplied by the scale factor. So, \( A'C'=k\times AC \).

Step2: Substitute Scale Factor

Substitute \( k = \frac{1}{2} \) into the formula: \( A'C'=\frac{1}{2}\times AC \), which can be rewritten as \( \frac{1}{2}(AC)=A'C' \).

Answer:

D. \(\frac{1}{2}(AC) = A'C'\)