Question

If A and B are (-2,-2) and (2,-4). Find the coordinates P such that AP=3/7 AB and P lies on the line segment ab

Answer 1

The coordinates of point P are
`(-(2)/(7), -(20)/(7))`.

Explanation:

Point P:

The coordinates of point P are (x,y).

AP=3/7 AB

So

`P - A = (3)/(7)(B-A)`

We apply this both for coordinate x and coordinate y.

Coordinate x:

`x - (-2) = (3)/(7)(2 - (-2))`

`x + 2 = (12)/(7)`

`x = (12)/(7) - 2 = (12)/(7) - (14)/(7) = -(2)/(7)`

Coordinate y:

`y - (-2) = (3)/(7)(-4 - (-2))`

`y + 2 = -(6)/(7)`

`y = -(6)/(7) - 2 = -(6)/(7) - (14)/(7) = -(20)/(7)`

The coordinates of point P are
`(-(2)/(7), -(20)/(7))`.