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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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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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).