Question

A point A(1,2) and B(3,4) are two end of line segment .find the point which devides AB in the Ratio 3:4​

Answer 1

We've been given two points A(1, 2) & B(3, 4), and we are asked to find the coordinates of the point which divides the line AB in the ratio 3 : 4.

Let the point which divides the line AB in the ration 3:4 be named D(x, y).

We can use the Section formula to find the coordinates of D(x, y).

$\rm \Longrightarrow D(x, y) = \Bigg(\dfrac{m_1x_2 + m_2x_1}{m_1 + m_2} , \dfrac{m_1y_2 + m_2y_1}{m_1 + m_2} \Bigg)$

Here, m₁ and m₂ stand for the ratio in which the line was divided, where m₁ = 3 and m₂ = 4. (m₁ : m₂ = 3 : 4)

And:

x₁ = 1

y₁ = 2

x₂ = 3

y₂ = 4

Now, substitute these values in the section formula.

$\rm \Longrightarrow D(x, y) = \Bigg(\dfrac{m_1x_2 + m_2x_1}{m_1 + m_2} , \dfrac{m_1y_2 + m_2y_1}{m_1 + m_2} \Bigg)$

$\rm \Longrightarrow D(x, y) = \Bigg(\dfrac{(3)(3) + (4)(1)}{3 + 4} , \dfrac{(3)(4) + (4)(2)}{3 + 4} \Bigg)$

$\rm \Longrightarrow D(x, y) = \Bigg(\dfrac{9 + 4}{7} , \dfrac{12 + 8}{7} \Bigg)$

$\rm \Longrightarrow D(x, y) = \Bigg(\dfrac{13}{7} , \dfrac{20}{7} \Bigg)$

Therefore, D(13/7, 20/7) divides the line joining A(1, 2) & B(3, 4) in the ratio 3 : 4.