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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(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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(i)Let P(x,y) divides the line segment joining the points A(-4,1), B(17,10) in the ratio 1:2,
Here x1 = -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 x1 = -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.
I hope this video will help solving this question!!!!
(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 ?