Question

A point P divides the line segment joining the points A(1, 3) and B(5, 9) in the ratio 1: 2, the co-ordinates of the point P are ______.

Options

• `(7/3, 5)`

• `(7, 5/3)`

• `(7/3, 5/3)`

• `(7/3, 13/3)`

Answer 1

A point P divides the line segment joining the points A(1, 3) and B(5, 9) in the ratio 1: 2, the co-ordinates of the point P are `bbunderline(7/3, 5)`.

Explanation:

Let point P be (x, y).

Given,

m₁ : m₂ = 1 : 2

By section-formula,

(x, y) = `((m_1x_2+m_2x_1)/(m_1+m_2), (m_1y_2+m_2y_1)/(m_1+m_2))`

Substituting values we get:

(x, y) = `((1 × 5 + 2 × 1)/(1 + 2), (1 × 9 + 2 × 3)/(1 + 2))`

= `((5 + 2)/3, (9 + 6)/3)`

= `(7/3, 15/3)`

= `(7/3, 5)`