This is the Important question of class 10 Based on Section Formula Chapter of M.L Aggarwal book for ICSE BOARD.
Any point divides the distance between two co-ordinates in a ratio. So calculate the co-ordinates of that point.
This is the Question Number 03, Exercise 11 of M.L Aggarwal.
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P divides the distance between A ( – 2, 1) and B (1, 4) in the ratio of 2 : 1. Calculate the co-ordinates of the point P.
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Let the co-ordinates of P(x, y) divides AB in the ratio m:n.
A(-2,1) and B(1,4) are the given points.
Given m:n = 2:1
x1 = -2 , y1 = 1 , x2 = 1 , y2 = 4 , m = 2 and n = 1
By Section formula x = (mx2+nx1)/(m+n)
x = (2×1+1×-2)/(2+1)
x = (2-2)/3
x = 0/3
x = 0
By Section formula y = (my2+ny1)/(m+n)
y = (2×4+1×1)/(2+1)
y = (8+1)/3
y = 9/3
y = 3
Hence the co-ordinate of point P are (0,3).