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Deepak Bora
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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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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.

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  1. 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

    3x= -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).

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