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प्रश्न
The midpoint of the line segment joining (2a, 4) and (-2, 2b) is (1, 2a+1). Find the value of a and b.
show that the points A(- 1, 2), B(2, 5) and C(- 5, – 2) are collinear.
उत्तर
Midpoint of (2a , 4) and (-2 , 2b) is (1 , 2a + 1)
x = `(x_1 + x_2)/(2)`
1 = `(2a - 2)/(2)`
1 = a - 1
∴ a = 2
y = `(y_1 + y_2)/(2)`
2a + 1 = `(4 + 2b)/(2)`
2a + 1 = 2 + b
∴ 5 - 2 = b
∴ b = 3
Therefore, a = 2, b = 3.
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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`.
