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# The line segment joining A (2, 3) and B (6, – 5) is intercepted by the x-axis at the point K. Write the ordinate of the point k. Hence, find the ratio in which K divides AB. Also, find the coordinates of the point K.

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This question is Based on Section Formula Chapter of M.L Aggarwal book for ICSE BOARD for class 10.
Here a line segment joining two points is intercepted by the x-axis at the point K.
Find the ordinate of the point K.
This is the Question Number 17, Exercise 11 of M.L Aggarwal.

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1. Since the point K is on X axis, its y co-ordinate is zero.

Let the point K be (x,0).

Let the point K divides the line segment joining A(2,3) and B(6,-5) in the ratio m:n.

Here x1 = 2 , y1 = 3 , x2 = 6, y2 = -5, y = 0

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

0 = (m×-5+n×3)/(m+n)

0 = (-5m+3n)/m+n

-5m+3n = 0

-5m = -3n

m/n = -3/-5 = 3/5

Hence the point K divides the line segment in the ratio 3:5.

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

x = (3×6+5×2)/(3+5)

x = (18+10)/8

x = 28/8 = 7/2

Hence the co-ordinates of K are (7/2, 0).

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