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Question
P is a point on the line joining A(4, 3) and B(–2, 6) such that 5AP = 2BP. Find the co-ordinates of P.
Solution
∵ 5AP = 2BP
`\implies (AP)/(BP) = 2/5`
`\implies` AP : PB = 2 : 5
Let the co-ordinates of P be (x, y) which divides the line joining the points A(4, 3) and B(–2, 6) in the ratio of 2 : 5
∴ `x = (2 xx (-2) + 5 xx 4)/(2 + 5)`
= `(-4 + 20)/7`
= `16/7`
`y = (2 xx 6 + 5 xx 3)/(2 + 5)`
= `(12 + 15)/7`
= `27/7`
∴ Co-ordinates of P are `(16/7, 27/7)`
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