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Question
Find the coordinates of a point P on the line segment joining A(1, 2) and B(6, 7) in such a way that AP = `2/5` AB
Solution
Let the point A(1, 2) and B(6, 7)
AP = `2/5` AB
`"AP"/"PB" = 2/5`
∴ AP = 2, PB = 5 – 2 = 3
A line divides internally in the ratio m : n
The point P = `(("m"x_2 + "n"x_1)/("m" + "n"), ("m"y_2 + "n"y_1)/("m" + "n"))`
m = 2, n = 3, x1 = 1, x2 = 6, y1 = 2, y2 = 7
The point P is (3, 4)
= `((2 xx 6 + 3 xx 1)/(2 + 3), (2 xx 7 + 3 xx 2)/(2 + 3))`
= `((12 + 3)/5, (14 + 6)/5)`
= `(15/5, 20/5)`
= (3, 4)
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