Question

triangle △abc is the image of △abc under a dilation with a scale factor of 2. what is the length of segment overline{ac}?

Explanation:

Step1: Recall the property of dilation

In a dilation, if the scale factor is \(k\), then the length of a segment in the original figure \(l\) and the length of the corresponding segment in the image \(l'\) satisfy the relation \(l'=k\times l\). Here, \(k = 2\).

Step2: Find the length of \(A'C'\)

Count the number of units between \(A'\) and \(C'\) on the grid. The vertical distance between \(A'\) and \(C'\) is \(6\) units. So \(A'C'=6\).

Step3: Calculate the length of \(AC\)

Since \(A'C'=k\times AC\) and \(k = 2\), \(A'C' = 6\), then \(AC=\frac{A'C'}{k}\). Substitute \(A'C' = 6\) and \(k=2\) into the formula: \(AC=\frac{6}{2}=3\).

Answer:

\(3\)