Question

2.) triangle abc is dilated. the dilated image is \\( \triangle a ^ { prime } b ^ { prime } c ^ { prime } \\). determine the value of x. show your work.

Explanation:

Step1: Set up proportion

Since the triangles are similar (due to dilation), \(\frac{AC}{A'C'}=\frac{BC}{B'C'}\). Substituting values: \(\frac{6}{4}=\frac{3}{x}\).

Step2: Cross - multiply

\(6x = 4\times3\).

Step3: Solve for \(x\)

\(6x=12\), then \(x=\frac{12}{6}\).

Answer:

\(x = 2\)