Given:
The two points are A(1, 3, −2) and C(4, −4, 4).
Point B divides AC in the ratio 1: 2.
To find:
The coordinates of B.
Solution:
If a point divides a lines segment in m:n, then the coordinates of that point are:
[tex]Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n},\dfrac{mz_2+nz_1}{m+n}\right)[/tex]
Point B divides AC in the ratio 1: 2. So, the coordinates of point B are:
[tex]Point=\left(\dfrac{1(4)+2(1)}{1+2},\dfrac{1(-4)+2(3)}{1+2},\dfrac{1(4)+2(-2)}{1+2}\right)[/tex]
[tex]Point=\left(\dfrac{4+2}{3},\dfrac{-4+6}{3},\dfrac{4-4}{3}\right)[/tex]
[tex]Point=\left(\dfrac{6}{3},\dfrac{2}{3},\dfrac{0}{3}\right)[/tex]
[tex]Point=\left(2,\dfrac{2}{3},0\right)[/tex]
Therefore, the coordinates of B are [tex]Point=\left(2,\dfrac{2}{3},0\right)[/tex].
