Question

In what ratio does the point (– 4, 6) divide the line segment joining the points A(– 6, 10) and B(3, – 8)?

Answer 1

Let the point given be P(-4,6). this point divides the line segment AB where A (-6,10) and B(3, -8).
According to the section formula:-
P(x) = m₁x₂+m₂x₁/m₁+m₂
-4 = m₁(3)+m₂(-6) /m₁+m₂
⇒ -4m₁-4m₂ = 3m₁-6m₂
⇒ -7m₁ = -2m₂
⇒ m₁/m₂ = 2/7
Hence the ratio in which AB is divided is 2:7.

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