Question

ilarity transformations
what is the length of \\(\overline{ac}\\)?
18 ft \t12 ft
4 ft \t3 ft

Explanation:

Step1: Identify Midsegment

Since \( M \) is the midpoint of \( AB \) (marks show \( AM = MB = 4\,\text{ft} \)) and \( N \) is the midpoint of \( BC \) (marks show \( BN = NC = 3\,\text{ft} \)), \( MN \) is the midsegment of \( \triangle ABC \).

Step2: Apply Midsegment Theorem

The Midsegment Theorem states that the midsegment of a triangle is parallel to the third side and half its length. So, \( MN=\frac{1}{2}AC \).

Step3: Solve for \( AC \)

Given \( MN = 6\,\text{ft} \), substitute into the formula:
\( 6=\frac{1}{2}AC \)
Multiply both sides by 2: \( AC = 6\times2 = 12\,\text{ft} \).

Answer:

12 ft