Question

The points which trisect the line segment joining the points $(0,0)$ and $(9,12)$ are

• A. $(3,4)$
• B. $(8,6)$
• C. $(6,8)$ and $(3,4)$
• D. $(4,0)$

Answer 1

The correct option is C $(6,8)$ and $(3,4)$

We know that by section formula, the co-ordinates of the points which divide internally the line segment joining the points $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio $m:n$ is

$(x,y)=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$

Let $A$ and $B$ be the points of trisection of the line segment joining the given points.

$\therefore$ Points trisecting the line segment joining $(0,0)$ and $(9,12)$ is $A(\frac{1\left(0\right)+2\left(9\right)}{2+1},\frac{1\left(0\right)+2\left(12\right)}{2+1})$ and $B(\frac{2\left(0\right)+1\left(9\right)}{1+2},\frac{2\left(0\right)+1\left(12\right)}{1+2})$

$⟹A(3,4)$ and $B(6,8)$