M.L Aggarwal book Important Question of class 10 chapter Based on Section Formula for ICSE BOARD.
You have to find two value for which mid-point of the line segment joining points are given.
This is the Question Number 10, Exercise 11 of M.L Aggarwal.
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The mid-point of the line segment joining the points (3m, 6) and ( – 4, 3n) is (1, 2m – 1). Find the values of m and n.
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Let the midpoint of line joining the points A(3m,6) and B(-4,3n) be C(1,2m-1).
Here x1 = 3m, y1 = 6 , x2 = -4, y2 = 3n
x = 1 , y = 2m-1
By Midpoint formula,
x = (x1+x2)/2
1 = (3m+-4)/2
3m-4 = 2
3m = 2+4
3m = 6
m = 6/3 = 2
By Midpoint formula,
y = (y1+y2)/2
2m-1 = (6+3n)/2
4m-2 = 6+3n
Put m = 2 in above equation
4×2-2 = 6+3n
8-2-6 = 3n
3n = 0
n = 0
Hence the value of m and n are 2 and 0 respectively.