Question

In what ratio y-axis divides the line segment joining the points (3, 4) and (– 2, 1)?

Answer 1

Let the given points be A(x₁, y₁) = (3, 4) and B(x₂, y₂) = (– 2, 1). Let m : n be the ratio in which the line segment is divided by y-axis (the coordinates of the point are (0,y))

∴ (0, y) = \(\big(\frac{mx_2 + mx_1} {m + n} , \frac{my_2 + my_1}{m + n}\big)\)

⇒ (0, y) = \(\big(\frac{3m + 3m} {m + n} , \frac{m + 4n}{m + n}\big)\)

⇒ 0 = \(\frac{−2m + 3n}{m + n}\) y = \(\frac{m + 4n}{m + n}\)

⇒ – 2m + 3n = 0

⇒ 2m = 3n

⇒ m : n = 3 : 2.