Question

The coordinates of the points P which divides (1, 0) and (0, 0) in 1 : 2 ratio are ____

• A. (2,3)
• B. $(\frac{2}{3},3)$
• C. (3, 2)
• D. $(\frac{2}{3},0)$

Answer 1

The correct option is D $(\frac{2}{3},0)$

Using the section formula, if a point $(x,y)$ divides the line joining the points $(x_1,y_1)$ and $(x_2,y_2)$ internally in the ratio $m:n$, then $(x,y)=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$
Substituting $(x_1,y_1)=(1,0)$ and $(x_2,y_2)=(0,0)$ and $m=1,n=2$ in the section formula, we get the point P $=(\frac{1\left(0\right)+2\left(1\right)}{1+2},\frac{1\left(0\right)+2\left(0\right)}{1+2})=(\frac{2}{3},0)$