Question

In what ratio is the line joining A(0, 3) and B(4, –1) divided by the x-axis? Write the co-ordinates of the point where AB intersects the x-axis.

Answer 1

Let the ratio be m₁ : m₂ when the x-axis intersects the line AB at P.

∴ Let co-ordinate of P(x, 0)

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

`x = (m_1 xx 4 + m_2 xx 0)/(m_1 + m_2), y = (m_1(-1) + m_2 xx 3)/(m_1 + m_2)`

`x = (4m_1)/(m_1 + m_2), y = (-m_1 + 3m_2)/(m_1 + m_2)`

∵ P lies on x-axis,

∴ y = 0

∴ `(-m_1 + 3m_2)/(m_1 + m_2) = 0`

`=>` – m₁ + 3m₂ = 0

`=>` m₁ = 3m₂

`=> m_1/m_2 = 3/1`

`=>` m₁ : m₂ = 3 : 1

Now, `x = (4 xx 3)/(3 + 1)`

= `12/4`

= 3

∴ Required co-ordinates of P will be (3, 0)