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.

Answer 1

From the given 

`"AP"/"AB" = 2/5`

⇒ `"AP"/"AB" = 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)