Find the point of trisection of the line segment joining the points (1, 2) and (11, 9) ? -Maths 9th

Find the point of trisection of the line segment joining the points (1, 2) and (11, 9) ? -Maths 9th
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1 Answer

Answer :

Let P divide AB in the ratio k : 1. Then, co-ordinates of P are \(\bigg(rac{7k+4}{k+1},rac{7k+4}{k+1}\bigg)\)But P ≡ (–1, –1)∴ \(rac{7k+4}{k+1}\) = -1 ⇒ 7k + 4 = – k – 1 ⇒ 8k = –5 ⇒ k = \(-rac{5}{8}\)∵ k is negative, it means that the division is external. ∴ AB is divided by P externally in the ratio \(rac{5}{8}\) : 1, i.e. 5 : 8.
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