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Question
The line joining the points A (–3, –10) and B (–2, 6) is divided by the point P such that `(PB)/(AB) = 1/5`. Find the co-ordinates of P.
Solution
Let the co-ordinates of P be (x, y) which divides the line joining the points A (–3, –10) and B (–2, 6) in the ratio of AP : PB i.e. (5 – 1) : 1 or 4 : 1
Since 5 PB = PA + PB
`\implies` 4 PB = PA
`\implies (PA)/(PB) = 4/1`
∴ `x = (4 xx (-2) + 1 xx (-3))/(4 + 1)`
= `(-8 - 3)/5`
= `(-11)/5`
`y = (4 xx 6 + 1 xx (-10))/(4 + 1)`
= `(24 - 10)/5`
= `14/5`
∴ Co-ordinates of P are `((-11)/5, 14/5)`
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Complete the following activity to find the coordinates of point P which divides seg AB in the ratio 3:1 where A(4, – 3) and B(8, 5).
Activity:
∴ By section formula,
∴ x = `("m"x_2 + "n"x_1)/square`,
∴ x = `(3 xx 8 + 1 xx 4)/(3 + 1)`,
= `(square + 4)/4`,
∴ x = `square`,
∴ y = `square/("m" + "n")`
∴ y = `(3 xx 5 + 1 xx (-3))/(3 + 1)`
= `(square - 3)/4`
∴ y = `square`
