Find the coordinates of the point which divides the line segment joining the points A (4,6),B (-3,1) in the ratio 2:3 internally.
Find also the coordinates of the point which divides `bar(AB)` in the same ratio externally.

Explanation

The coordination of the point P is `
`((mx_2+nx_1)/(m+n),(my_2+ny_1)/(m+n))` `((2(-3)+3.4)/(2+3), (2.1+3.6)/(2+3))`
`(6/5,20/5)=(6/5,4)`
If the point C divides `bar^AB` externally in the ratio 2:3, then the coordinates of the point C is
`((mx_2+nx_1)/(m-n),(my_2-ny_1)/(m-n))`
`((2(-3)-3.4)/(2-3),(2.1-3.6)/(2-3))`
`((-6-12)/-1,(2-18)/-1)=(18,16)`.