Question

plz Fast, most important!!!!!
A , B, and c are collinear . B lies between A and C . A is at (A, -8) , B is at (B, -6) C is (15, 7) find the ratio between AB / BC by section formula​

Answer 1

It has given that, A , B and C are collinear , B lies between A and C , A is at (a, -8) , B is at (b, -6) and C is (15, 7).

we have to find the ratio AB/BC by section formula.

solution : here , A , B and C are collinear means, all the three points lying in the same line. also said, B lies between A and C.

so, A ------- B ----------- C

now using section formula,

(x, y) = [(λx₂ + x₁)/(λ + 1), (λy₂ + y₁)/(λ + 1)]

⇒(B, -6) = [(λ × 15 + A)/(λ + 1), (λ × 7 - 8)/(λ + 1)]

-6 = (7λ - 8)/(λ +1)

⇒-6λ - 6 = 7λ - 8

⇒-13λ = -2

⇒λ = 2/13

Therefore the ratio AB/B is 2 : 13