Determine the ratio in which the point P(m, 6) divides the join of A(– 4, 3) and B(2, 8). Also find the value of m. -Maths 9th

Determine the ratio in which the point P(m, 6) divides the join of A(– 4, 3) and B(2, 8). Also find the value of m. -Maths 9th
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Answer :

(b) 1 : 2Any point on the x-axis is (a, 0).Let the point (a, 0) divide the join of A(2, –3) and B(5, 6) in the ratio k : 1. Then the co-ordinates of the point of division are \(\bigg(rac{5k+2}{k+1},rac{6k-3}{k+1}\bigg)\)Now, \(rac{5k+2}{k+1}\) = a and \(rac{6k-3}{k+1}\) = 0∴ 6k – 3 = 0 ⇒ k = \(rac{1}{2}\)Required ratio is k : 1 ⇒ \(rac{1}{2}\) : 1 = 1 : 2.
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