Question

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.

Answer 1

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`