Question

Points A, B, and C are collinear. Point B is the midpoint of AC. Find the length of AB.

AB = 3x
BC = 4x − 6

Answer 1

AB = 18

Explanation:

To find:-

• The length of AB .

Answer:-

We are here given that points A , B and C are collinear and B is the midpoint of AC . From the data provided in the question we have;

• AB = 3x
• BC = 4x - 6 .

Since B is the midpoint of AC, it will divide AC into two equal parts namely AB and BC. And these parts will be equal to one another. ( By Euclid's first axiom, Things which are half of the same thing are equal to one another.)

So we have;

`\sf:\implies AB = BC \\`

`\sf:\implies 3x = 4x - 6 \\`

`\sf:\implies 3x -4x = -6 \\`

`\sf:\implies -x = -6 \\`

`\sf:\implies\red{ x = 6} \\`

Finally plug in the value of x, in the given expression of AB as ,

`\sf:\implies AB = 3(x) \\`

`\sf:\implies AB = 3(6) \\`

`\sf:\implies \red{AB = 18} \\`

Hence the value of AB is 18 .

Answer 2

• 18 units

Explanation:

As per question, point B is the midpoint of AC.

According to definition of midpoint, AB = BC:

• 3x = 4x - 6
• 4x - 3x = 6
• x = 6

The length of AB is:

• AB = 3*6 = 18