# The coordinates of a point dividing the line segment joining

The coordinates of a point dividing the line segment joining (1, 2, 3) and (4, 5, 6) internally in the ratio 2:1 is ____________________

A. (3, 4, 5)

B. (5, 4, 3)

C. (5, 3, 4)

D. (4, 5, 3)

I have been asked this question in a job interview.

I would like to ask this question from Three Dimensional Geometry topic in section Three Dimensional Geometry of Mathematics – Class 11

The correct choice is A. (3, 4, 5)

For explanation I would say: The coordinates of a point dividing the line segment joining (x1, y1, z1) and (x2, y2, z2) internally in the ratio m : n is $$(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n},\frac{mz_2+nz_1}{m+n})$$.

So, the coordinates of a point dividing the line segment joining (1, 2, 3) and (4, 5, 6) internally in the ratio 2:1 is $$(\frac{2*4+1*1}{2+1},\frac{2*5+1*2}{2+1},\frac{2*6+1*3}{2+1})$$ = (3, 4, 5).