The midpoint P of the line segment joining the points A(– 10, 4) and B(– 2, 0) lies on the line segment joining the points C(– 9, – 4) and D(– 4, y). Find the ratio in which P divides CD. Also, find the value of y.

Question

Philoid · Accepted Answer

For P(x,y)

X = (– 10 – 2)/2 = – 6

Y = (4 + 0)/2 = 2

Thus, P(– 6,2)

Now

– 6 = (m₁x₂ + m₂x₁)/ m₁ + m₂

– 6 = (m₁(– 4) + m₂(– 9))/ m₁ + m₂

– 6 = (– 4m₁ – 9m₂)/ m₁ + m₂

– 6(m₁ + m₂) = – 4 m₁ – 9 m₂

– 2m₁ = – 3m₂

m₁:m₂ = 3:2,

2 = (m₁y₂ + m₂y₁)/ m₁ + m₂

2 = (3 × y + 2x (– 4))/5

2 = (3y – 8)/5

10 = 3y – 8

3y = 18

y = 6