The line segment joining A(6,3) to B(-1,-4) is doubled in length by having half its length added to each end. Find the coordinates of the new ends.

Let P and Q be the required new ends

Coordinates of P

Let AP = k

∴ AB = 2AP = 2k

and PB = AP + AB = k + 2k = 3k

∴ P divides AB externally in the ratio 1:3

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

…(i)

Here, m₁ = 1, m₂ = 3

(x₁, y₁) = (6, 3) and (x₂, y₂) = (-1, -4)

Putting the above values in the above formula, we get

∴Coordinates of P are

Coordinates of Q.

Q divides AB externally in the ratio 3:1

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

…(i)

Here, m₁ = 3, m₂ = 1

(x₁, y₁) = (6, 3) and (x₂, y₂) = (-1, -4)

Putting the above values in the above formula, we get

∴Coordinates of Q are