An Important Question of class 10 Based on Section Formula Chapter of M.L Aggarwal for ICSE BOARD.
Here given that a line segment joining two points.
Find the ratio in which that line segment is divided by the y-axis and also find the coordinates of the point of intersection and lenght of that line segment.
This is the Question Number 20, Exercise 11 of M.L Aggarwal.
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Given a line segment AB joining the points A ( – 4, 6) and B (8, – 3). Find: (i) the ratio in which AB is divided by the y-axis. (ii) find the coordinates of the point of intersection. (iii)the length of AB.
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(i) Let m:n be the ratio in which the line segment joining A (-4,6) and B(8,-3) is divided by the Y axis.
Since the line meets Y axis, its x co-ordinate is zero.
Here x1 = -4, y1 = 6
x2 = 8, y2 = -3
By section formula, x = (mx2+nx1)/(m+n)
0 = (m×8+n×-4)/(m+n)
0 = (8m+-4n)/(m+n)
0 = 8m+-4n
8m = 4n
m/n = 4/8 = 1/2
Hence the ration m:n is 1:2.
(ii) By Section formula y = (my2+ny1)/(m+n)
Substitute m and n in above equation
y = (1×-3+2×6)/(1+2)
y = (-3+12)/3
y = 9/3 = 3
So the co-ordinates of the point of intersection are (0,3).
(iii) By distance formula, d(AB) = √[(x2-x1)2+(y2-y1)2]
d(AB) = √[(8-(-4))2+(-3-6)2]
d(AB) = √[(12)2+(-9)2]
d(AB) = √(144+81)
d(AB) = √225
d(AB) = 15
Hence the length of AB is 15 units.