Question

Find the coordinates of the point which divides the line segment joining (2,4) and (6,8) in the ratio 1:3 internally and externally.

Answer 1

Let P(x,y) be the point which divides the line segment internally.

Using the section formula for the internal division, i.e.

Here, m₁ = 1, m₂ = 3

(x₁, y₁) = (2, 4) and (x₂, y₂) = (6, 8)

Putting the above values in the above formula, we get

⇒ x = 3, y = 5

Hence, (3,5) is the point which divides the line segment internally.

Now, Let Q(x,y) be the point which divides the line segment externally.

Using the section formula for the external division, i.e.

Here, m₁ = 1, m₂ = 3

(x₁, y₁) = (2, 4) and (x₂, y₂) = (6, 8)

Putting the above values in the above formula, we get

Hence, (0,2) is the point which divides the line segment externally.