Determine the ratio in which 2x +3y – 30 = 0 divides the join of A(3, 4) and B(7, 8) and at what point? -Maths 9th

Determine the ratio in which 2x +3y – 30 = 0 divides the join of A(3, 4) and B(7, 8) and at what point? -Maths 9th
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Answer :

Let A(1, 2) and B(11, 9) be the given points. Let the points of trisection be P and Q. Then,AP = PQ = QB = k (say)⇒ AQ = AP + PQ = 2k and PB = PQ + QB = 2k ∴ AP : PB = k : 2k = 1 : 2 and AQ : QB = 2k : k = 2 : 1 ⇒ P divides AB internally in the ratio 1 : 2 and Q divides AB internally in the ratio 2 : 1.∴ Coordinates of P are \(\bigg[rac{1 imes11+2 imes1}{1+2},rac{1 imes9+2 imes2}{1+2}\bigg]\), i.e \(\big(rac{13}{3},rac{13}{3}\big)\)Coordinates of Q are \(\bigg[rac{2 imes11+1 imes1}{2+1},rac{2 imes9+1 imes2}{2+1}\bigg]\), i.e \(\big(rac{23}{3},rac{20}{3}\big)\)Hence, the two points of trisection are \(\big(rac{13}{3},rac{13}{3}\big)\) and \(\big(rac{23}{3},rac{20}{3}\big)\).
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