If A (4,-8), B (3,6) and C(5,-4) are the vertices of a ΔABC, D is the mid-point of BC and P is a point on AD joined such that , find the coordinates of P.

Given: D is the midpoint of BC. So, BD = DC

Then the coordinates of D are

⇒ x = 4 and y = 1

So, coordinates of D are (4, 1)

Now, we have to find the coordinates of P.

Given:

⇒ m₁ = 2 and m₂ = 1

and (x₁, y₁) = (4, -8) ; (x₂, y₂) = (4, 1)

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

…(i)

⇒ x = 4, y = -2

Hence, the coordinates of P are P(x,y) = P(4, -2)