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प्रश्न
In the given figure, P(4, 2) is mid-point of line segment AB. Find the co-ordinates of A and B.
उत्तर
Point A lies on x-axis, so let its co-ordinates be (x, 0).
Point B lies on y-axis, so let its co-ordinates be (0, y).
P(4, 2) is mid-point of line segment AB.
∴ `(4, 2) = ((x + 0)/2, (0 + y)/2)`
`=> 4 = x/2` and `2 = y/2`
`=>` 8 = x and 4 = y
Hence, the co-ordinates of points A and B are (8, 0) and (0, 4) respectively.
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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`.
