Question

M is the midpoint of AB If MA = 2x -5 and MB = 3x - 13. (Hint: draw a diagram!)

x =
MA =
AB=​

Answer 1

x = 8

MA = 11 units

AB =​ 22 units

====================

We are given that:

• M is the midpoint of segment AB
• MA = 2x - 5
• MB = 3x - 13

We need to find the value of x and length of segments MA and AB.

Use the property of the midpoint:

• Midpoint is equidistant from the endpoints.

It means that:

• MA = MB and

• AB = 2*MA or AB = 2*MB

Substitute values into first equation and solve for x:

• 2x - 5 = 3x - 13
• 3x - 2x = 13 - 5
• x = 8

Now find the length of required segments:

• MA = 2*8 - 5 = 16 - 5 = 11 units

• AB = 2*MA = 2*11 = 22 units