Question

M is the midpoint of segment AB. If AM = 2x + 1 and MB = 4x - 3, find AB.

Answer 1

AB = 10

Explanation:

M being the midpoint of segment AB means that:

AB = AM + MB

And

AM = MB

We have that:

AM = 2x + 1

MB = 4x - 3

Since AM = MB

2x + 1 = 4x - 3

4x - 2x = 1 + 3

2x = 4

x = 4/2

x = 2

So

AB = AM + MB

AM = 2x + 1 = 2*2 + 1 = 5

MB = 4x - 3 = 4*2 - 3 = 5

AB = 5 + 5 = 10