Question

Draw a figure to use for numbers 13 - 15. Points A. B. and C are collinear and Bis the midpoint of AC. 13. If AB = 3x - 8 and BC = x + 4, find the length of AB 14. If BC = 6x - 7 and AB = 5x + 1. find the length of AC 15. If AB = 8x + 11 and BC = 12x - 1. find the length of BCAnswer 13

Answer 1

13.

Given:

AB = 3x - 8, BC = x + 4

A, B and C are collinear

B is a midpoint of AC

Since B is the midpoint, we can write:

`\text{length of AB = Length of BC}`

Hence, we have:

`3x\text{ - 8 = x + 4}`

Solving for x:

`\begin{gathered} \text{Collect like terms} \\ 3x\text{ -x = 4 + 8} \\ 2x\text{ = 12} \\ \text{Divide both sides by 2} \\ x\text{ = 6} \end{gathered}`

Hence, the length of AB is:

`\begin{gathered} =\text{ 3x - 8} \\ =\text{ 3}*\text{ 6 -8} \\ =\text{ 18 -8} \\ =\text{ 10} \end{gathered}`

Answer:

The length of AB is 10 unit