Find the coordinates of the point which divides the line segments joining the points `(6,3)` and `(-4,5)` in the ratio `3:2` (i) internally and (ii) externally.

Explanation

(i) Given points are A (6,3) and B(-4,5). Let poitn P(x,y) divide AB internally in the ratio `3:2`

`therefore (x,y)-=((3(-4)+2(6))/(3+2),(3(5)+2(3))/(3+2))-=(0,(21)/(5))`
(ii) `P(x,y)` divides AB externally in the ratio `3:2`.

`therefore(x,y)-=((3(-4)-2(6))/(3-2),(3(5)-2(3))/(3-2))-=(-24,9)`
Alternatively, `(AB)/(BP)=(1/2)` (From the figure)
`therefore(-4,5)-=((3(6)+1(x))/(2+1),(2(3)+1(y))/(2+1))-=((12+x)/(3),(6+y)/(3))`
`therefore (x,y)-=(-24,9)`