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 x

_{1 }= -4, y_{1}= 6x

_{2}= 8, y_{2}= -3By section formula,x = (mx_{2}+nx_{1})/(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 = (my

_{2}+ny_{1})/(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) = √[(x

_{2}-x_{1})^{2}+(y_{2}-y_{1})^{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.