Find the coordinates of the points which divide the line segment joining A(2, –3) and B(–4, –6) into three equal parts.

Question

Philoid · Accepted Answer

Let the P(a, b) and Q(c, d) divide the line segment AB in three equal parts.

Observation:

P divides AB in 1:2

Section formula

If a point P(x, y) divides a line segment joining A(x₁, y₁) and B(x₂, y₂) in a ratio m:n, then coordinates of P are

Hence, Coordinates of P:

Also, Q is the mid-point of PB

we know that, mid-point of line joining the points (x_1, y₁) and (x₂, y₂) is

Hence, coordinates of Q:

⇒ (c, d) = (–2, –5)