Question

If the line joining the points A(4, –5) and B(4, 5) is divided by the point P such that `(AP)/(AB) = (2)/(5)`, find the coordinates of P.

The line segment joining the points A (4, –5) and B (4, 5) is divided by the point P such that AP : AB = 2 : 5. Find the coordinates of Р.

Answer 1

From the given 

`(AP)/(AB) = 2/5`

⇒ `(AB)/(AP) = 5/2`

`(AB)/(AP) - 1 = 5/2 - 1`

⇒ `(PB)/(AP) = 3/2`

∴ Coordinates of P

= `((mx_2+nx_1)/(m+x), (my_2+xy_1)/(m+x))`

= `((2xx4+3xx4)/(2+3), (2xx5+3xx(-5))/(2+3))`

= `((8+12)/5, (10-15)/5)`

= (4, –1)