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.

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

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

…(i)

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.

…(i)

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 = 0, y = 2

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