Question

what is the length of fg, when m is the midpoint of fg?

Explanation:

Step1: Use mid - point property

Since \(M\) is the mid - point of \(FG\), then \(FM = MG\). So we set up the equation \(5x + 13=5 - 3x\).

Step2: Solve the equation for \(x\)

Add \(3x\) to both sides: \(5x+3x + 13=5-3x + 3x\), which simplifies to \(8x+13 = 5\). Then subtract 13 from both sides: \(8x+13 - 13=5 - 13\), getting \(8x=-8\). Divide both sides by 8: \(x=\frac{-8}{8}=-1\).

Step3: Find the length of \(FM\) or \(MG\)

Substitute \(x = - 1\) into the expression for \(FM\): \(FM=5x + 13=5\times(-1)+13=-5 + 13 = 8\). (We could also use the expression for \(MG\): \(MG = 5-3x=5-3\times(-1)=5 + 3 = 8\)).

Step4: Calculate the length of \(FG\)

Since \(FG=FM + MG\) and \(FM = MG = 8\), then \(FG=8 + 8=16\).

Answer:

16