Question

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

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

Answer 1

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

We know that if a point $P(x,y)$ divides the line segment $AB$ joining the points $A(x_1,y_1)\&B(x_2,y_2)$ in the ratio $m:n$ then, by the section formula, we have

$x=\frac{n{x}_1+m{x}_2}{m+n}\&y=\frac{n{y}_1+m{y}_2}{m+n}.$

Hence, $m=1,n=2,A=(1,0)$ and $B=(0,0)$

Let $P(x,y)$ be the required point.

$\therefore$ $x=\frac{(1\times 0)+(2\times 1)}{1+2}=\frac{0+2}{3}=\frac{2}{3}$

and

$y=\frac{(1\times 0)+(2\times 0)}{1+2}=\frac{0+0}{3}=0$

Therefore, the coordinates of the point is $(\frac{2}{3},0)$.