This is the Important question of class 10 Based on Section Formula Chapter of M.L Aggarwal book for ICSE BOARD.
Here you have to find a point for which any point divides the line segment joining a point in some ratio.
This is the Question Number 15, Exercise 11 of M.L Aggarwal.
Deepak BoraNewbie
The point P ( – 4, 1) divides the line segment joining the points A (2, – 2) and B in the ratio of 3 : 5. Find the point B.
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Let the co-ordinates of B be (x2,y2).
Given co-ordinates of A = (2,-2)
Co-ordinates of P = (-4,1)
Ratio m:n = 3:5
x1 = 2, y1 = -2, x = -4, y = 1
P divides AB in the ratio 3:5
By section formula, x = (mx2+nx1)/(m+n)
-4 = (3×x2+5×2)/(3+5)
-4 = (3x2+10)/8
-32 = 3x2+10
3x2 = -32-10 = -42
x2 = -42/3 = -14
By Section formula y = (my2+ny1)/(m+n)
1= (3×y2+5×-2)/(3+5)
1 = (3y2-10)/8
8 = 3y2-10
3y2 = 8+10 = 18
y = 18/3 = 6
Hence the co-ordinates of B are (-14,6).