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# (i) Write down the co-ordinates of the point P that divides the line joining A ( – 4, 1) and B (17,10) in the ratio 1 : 2. (ii)Calculate the distance OP where O is the origin. (iii)In what ratio does the y-axis divide the line AB ?

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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 the co-ordinates of a point that divides the line joining two points in a ratio.
Solve this question.
This is the Question Number 21, Exercise 11 of M.L Aggarwal.

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1. (i)Let P(x,y) divides the line segment joining the points A(-4,1), B(17,10) in the ratio 1:2,

Here x= -4, y1 = 1

x2 = 17, y2 = 10

m:n = 1:2

By section formula, x = (mx2+nx1)/(m+n)

x = (1×17+2×-4)/(1+2)

x = (17+-8)/3

x = 9/3

x = 3

By Section formula y = (my2+ny1)/(m+n)

y = (1×10+2×1)/(1+2)

y = (10+2)/3

y = 12/3 = 4

Hence the co-ordinates of the point P are (3,4).

(ii)Since O is the origin, the co-ordinates of O are (0,0).

By distance formula, d(OP) = √[(x2-x1)2+(y2-y1)2]

d(OP) = √[(0-3)2+(0-4)2]

d(OP) = √[(3)2+(4)2]

d(OP) = √(9+16)

d(OP) = √25 = 5

Hence the distance OP is 5 units.

(iii)Let m:n be the ratio in which Y axis divide line AB.

Since AB touches Y axis, its x co-ordinate will be zero.

Here x= -4, y1 = 1

x2 = 17, y2 = 10

By section formula, x = (mx2+nx1)/(m+n)

0 = (m×17+n×-4)/(m+n)

0 = (17m-4n)/(m+n)

17m-4n = 0

17 m = 4n

m/n = 4/17

m:n = 4:17

Hence the ratio in which Y axis divide line AB is 4:17.

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