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प्रश्न
A lies on the x - axis amd B lies on the y -axis . The midpoint of the line segment AB is (4 , -3). Find the coordinates of A and B .
उत्तर
Coordinates of B are (14 , 6)
Let (x , 0) lies on the x - axis and B (0 , y) lies on y - axis , given AP : PB = 1 : 1
Coordinates of P are ,
P (4 , -3) = P `(("x" + 0)/2 , (0 + "y")/2)`
`4 = "x"/2 , , -3 = 4/2`
x = 8 , y = -6
Co-ordinates of A are (8 , 0) and B are (0 , -6)
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Solution :
Suppose, (–4, 2) = (x1, y1) and (6, 2) = (x2, y2) and co-ordinates of P are (x, y).
∴ According to the midpoint theorem,
x = `(x_1 + x_2)/2 = (square + 6)/2 = square/2 = square`
y = `(y_1 + y_2)/2 = (2 + square)/2 = 4/2 = square`
∴ Co-ordinates of midpoint P are `square`.
