Question

dilate △abc by a scale factor of \\( \frac { 1 } { 2 } \\) with the center of dilation at point c.
to dilate the triangle, think about the lengths of the corresponding sides.
what is the length of \\( a ^ { \prime } c \\), the image of segment ac?
\\( a ^ { \prime } c = \\) units

Explanation:

Step1: Calculate the length of \( AC \)

From the graph, the length of \( AC \) is \( 8 \) units.

Step2: Use the dilation formula

The formula for dilation is \( A'C=\text{scale factor}\times AC \). Given the scale factor \( k = \frac{1}{2} \) and \( AC = 8 \), then \( A'C=\frac{1}{2}\times8 \).

$$A'C = 4$$

Answer:

\(4\)