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प्रश्न
A and B are two points on the x-axis and y-axis respectively. P (2, −3) is the midpoint of AB. Find the:
(1) coordinates of A and B
(2) slope of line AB.
(3) an equation of line AB.
उत्तर
1) Let the coordinates be A(x, 0) and B(0, y).
Mid-point of A and B is given by `((x+0)/2 , (y + 0)/2) = (x/2, y/2)`
`=> (2, -3) = (x/2, y/2)`
=> `x/2 = 2` and `y/2 = -3`
=> x = 4 and y = 6
∴ A(4,0) and B(0,-6)
2) Slope of line AB, m = `(y_2 - y_1)/(x_2 - x_1) = (-6-0)/(0-4) = 3/2`
3) Equation of line AB, using A(4,0)
`y - 0 = 3/2 (x - 4) => 3x - 2y = 12`
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