Question

Given collinear points A B, and C such that point B is between A and C. Find the length of AB given that AB = 5x + 1, BC = 3x-4, and AC = x + 11

Answer 1

Given collinear points A B, and C such that point B is between A and C.

Collinear points mean they all lie on the same plane.

AB = 5x + 1

BC = 3x-4

AC = x + 11​

We are asked to find the length of AB.

To find the length of AB it is necessary to first find the value of x.

Let us draw this scenario to better understand the problem.

As you can see in the above figure, the sum of the length AB and BC must be equal to the length AC.

Mathematically,

`AB+BC=AC`

Let us substitute the given values

`(5x+1)+(3x-4)=x+11`

Now let's solve the equation for x.

`\begin{gathered} 5x+1+3x-4=x+11 \\ 5x+3x+1-4=x+11 \\ 8x-3=x+11 \\ 8x-x=11+3 \\ 7x=14 \\ x=(14)/(7) \\ x=2 \end{gathered}`

Finally, the length of AB is

`\begin{gathered} AB=5x+1 \\ AB=5\mleft(2\mright)+1 \\ AB=10+1 \\ AB=11 \end{gathered}`

Therefore, the length of AB is 11.