Question

Find the co-ordinates of the point dividing the join of $A(1,-2)$ and $B(4,7)$ externally in the ratio of $2:1.$

• A. $(7,16)$
• B. $(7,12)$
• C. $(3,\frac{16}{3})$
• D. $(3,16)$

Answer 1

The correct option is A $(7,16)$

The given points are $A(1,-2)$ and $B(4,7)$.

We have to find the coordinate of points which divide the line segment externally in the ratio $2:1$

Let point $C$ divides the segment $AB$ in the ratio $1:2$, hence $m=2,n=1$

By section formula which states that when the line segment is divided externally by the point in the ration $m:n$ then coordinates of point are

$\Rightarrow$ $C=(\frac{m{x}_2-n{x}_1}{m-n},\frac{m{y}_2-n_1}{m-n})$

$=(\frac{\left(2\right)\left(4\right)-\left(1\right)\left(1\right)}{2-1},\frac{\left(2\right)\left(7\right)-\left(1\right)(-2)}{2-1})$

$=(\frac{7}{1},\frac{16}{1})$

$=(7,16)$