This is the Important question of class 10 Based on Section Formula Chapter of M.L Aggarwal book for ICSE BOARD.
A line segment joining two points is a diameter of a circle with a centre
So find the co-ordinates of the centre point.
This is the Question Number 09, Exercise 11 of M.L Aggarwal
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The line segment joining A ( – 3, 1) and B (5, – 4) is a diameter of a circle whose centre is C. find the co-ordinates of the point C.
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Given Co-ordinates of A = (-3,1)
Co-ordinates of B = (5,-4)
Here x1 = -3, y1 = 1 , x2 = 5, y2 = -4
Let C(x,y) be the midpoint of AB
By midpoint formula,
x = (x1+x2)/2
y = (y1+y2)/2
x = (-3+5)/2 = 2/2 = 1
y = (1+-4)/2 = -3/2
Hence the co-ordinate of midpoint of AB is C(1,-3/2) .