Question

e is the midpoint of (overline{df}). if (de = 3x) and (ef=x + 2), what is (ef)?
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use the midpoint property

Since \(E\) is the midpoint of \(\overline{DF}\), \(DE = EF\). So, \(3x=x + 2\).

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides: \(3x-x=x + 2-x\), which gives \(2x=2\).
Divide both sides by \(2\): \(x=\frac{2}{2}=1\).

Step3: Find the value of \(EF\)

Substitute \(x = 1\) into \(EF=x + 2\). So, \(EF=1+2\).

Answer:

\(3\)