Question

Find the ratio where point (-3, P), divides internally the line segment which joins points (-5, -4) and (-2, 3). Also find P.

Answer 1

Let the point P(-3, p) divides the line segment joining the points A(-5, -4) and B(-2, 3) internally in the ratio m₁ : m₂.

Hence, x co-ordinate of point P(-3, p)

= -3(m₁ + m₂) = -2m₁ – 5m₂

⇒ -3m₁ – 3m₂ = -2m₁ – 5m₂

⇒ -3m₁ + 2m₁ = -5m₂ + 3m₂

⇒ – m₁ = -2m₂

⇒ m₁/m₂ = -2/-1 = 2/1

Hence required ratio m₁ : m₂ = 2 : 1

Now, y co-ordinate of point P(-3, p)

Hence, required ratio 2 : 1 and p = 2/3