Question

The points `A(3, 5)` and `C (12, 2)` are points on the straight line `ABC.` `AB:BC = 2:1`. What are the coordinates of `B`?

Answer 1

The coordinates of `B` are `(9,3)`

Explanation:

If the line joining two points `(x_1,y_1)` and `(x_2,y_2)` is divided in the ratio `l:m`, the coordinates of point dividing the line are

`((mx_1+lx_2)/(l+m),(my_1+ly_2)/(l+m))`

Hence, as we are dividing the line joining point `A(3,5)` and `C(12,2)` in the ratio of `2:1`, the coordinates of dividing point `B` are

`((1xx3+2xx12)/(2+1),(1xx5+2xx2)/(2+1))`

or `((3+24)/3,(5+4)/3)`

or `(9,3)`