If the point lies on the line segment joining the points A(3, – 5) and B(– 7, 9) then find the ratio in which P divides AB. Also, find the value of y.

Question

Philoid · Accepted Answer

Given: The points P(1/2, y) lies on the line AB.

Then,

1/2 = (m₁x₂ + m₂x₁)/ m₁ + m₂

1/2 = (m₁(– 7) + m₂3)/ m₁ + m₂

1/2 = (– 7m₁ + 3m₂)/ m₁ + m₂

(m₁ + m₂) = – 14 m₁ + 6 m₂

15m₁ = 5m₂

m₁: m₂ = 3:5

y = (m₁y₂ + m₂y₁)/ m₁ + m₂

y = (3 × 9 + 5x (– 5))/3 + 5

y = (27 – 25)/8

y = 2/8

y = 1/4