Question

If A = (−4, 3) and B = (8, −6)

1. Find the length of AB.
2. In what ratio is the line joining A and B, divided by the x-axis?

If A = (−4, 3) and B = (8, −6), find the length of AB.

Answer 1

i. A (−4, 3) and B (8, −6)

`AB = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`

= `sqrt((8 + 4)^2 + (-6 - 3)^2)`

= `sqrt(144 + 81)`

= `sqrt(225)`

= 15 units

ii. Let P be the point, which divides AB on the x-axis in the ratio k : 1.

Therefore, y-co-ordinate of P = 0.

`=> (-6k + 3)/(k + 1) = 0`

`=> -6k + 3 = 0`

`=> k = 1/2`

∴ Required ratio is 1 : 2.