Question

1. the midpoint of jk is m(...) 15. point m is the midpoint of (overline{ab}), where (am = 3x + 8) and (mb = 6x - 4). find (ab).

Explanation:

Step1: Use midpoint property (AM = MB)

Since M is the midpoint of \(\overline{AB}\), \(AM = MB\). So we set up the equation:
\(3x + 8 = 6x - 4\)

Step2: Solve for x

Subtract \(3x\) from both sides:
\(8 = 3x - 4\)
Add 4 to both sides:
\(12 = 3x\)
Divide both sides by 3:
\(x = 4\)

Step3: Find AM and MB

First, find \(AM\) by substituting \(x = 4\) into \(3x + 8\):
\(AM = 3(4)+8 = 12 + 8 = 20\)
Since \(AM = MB\), \(MB = 20\)

Step4: Find AB (AM + MB)

\(AB = AM + MB = 20 + 20 = 40\)

Answer:

\(40\)