Question

A and B are two points on the x-axis and y-axis respectively. P(2, −3) is the mid point of AB. Find the

1. co-ordinates of A and B
2. slope of line AB
3. equation of line AB.

Answer 1

i. Let the co-ordinates 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)

ii. Slope of line AB, m = `(y_2 - y_1)/(x_2 -x_1)`

= `(-6 - 0)/(0 - 4)`

= `3/2`

= `1 1/2`

iii. Equation of line AB, using A(4, 0)

y – y₁ = m(x – x₁)

`y - 0 = 3/2 (x - 4)`

2y = 3x – 12

3x – 2y = 12