Question

Find the co-ordinates of the points which divide internally the line segment joining the points $(1,7)$ and $(6,-3)$ in the ratio $2:3$.

• A. $(2,3)$
• B. $(3,3)$
• C. $(2,5)$
• D. None of these

Answer 1

The correct option is B $(3,3)$

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

We know that, 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

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

Here, $x_1=1,y_1=7x_2=6,y_2=-3$

and $m=2,n=3$

$x=\frac{3+12}{5}=3$ and $y=\frac{21-6}{5}=3$.

Hence the required point is $P(3,3)$