Question

Find the ratio in which (p,4) divides the line segment joining the points

Answer 1

A(2,3) ------------------P(4,m)--------------B(6,-3)

Applying section formula ,

Let λ is the ratio by which P divides the line joining A and B.

x = (λx₂ + x₁)/(λ + 1)

here , x = 4 , x₁ = 2 , x₂ = 6

Now, 4 = (6λ + 2)/(λ + 1)

4(λ + 1) = 6λ + 2

4λ + 4 = 6λ + 2

2 = 2λ ⇒ λ = 1

Hence, p divides the line AB into 1 : 1 ratio.

Now, for y - co - ordinate

y = (λy₂ + y₁)/(λ + 1)

m = (1 × -3 + 3)/(1 + 1) = 0

Hence , m = 0