In what ratio is the line segment joining A(2, – 3) and B(5, 6) divided by the x – axis? Also, find the coordinates of the point of division.

Question

Philoid · Accepted Answer

The segment is divided by x – axis i.e the coordinates are (x,0)

x = (m₁x₂ + m₂x₁)/ m₁ + m₂

x = (m₁ × 5 + m₂ 2)/ m₁ + m₂

x = (5m₁ + 2m₂ ) / m₁ + m₂

5m₁ + 2m₂ = x(m₁ + m₂ )

(5 – x)m₁ + (2 – x)m₂ = 0

0 = (m₁y₂ + m₂y₁)/ m₁ + m₂

0 = (m₁ × 6 + m₂(– 3))/ m₁ + m₂

0 = (6m₁ – 3m₂ ) / m₁ + m₂

6m₁ – 3m₂ = 0

Solving for m₁ and m₂ we get

m₁ = 1

m₂ = 2

(1 : 2),

Putting the values of m₁ and m₂

x = 3

Hence coordinates are (3,0)