Question

The co-ordinates of the point B which divides segment PQ joining the points $P(-2,-4)$ and $Q(-2,-1)$ in the ratio $m:n=2:5$, are

• A. $B(x,y)=(2,6)$
• B. $B(x,y)=(-2,6)$
• C. $B(x,y)=(2,-6)$
• D. $B(x,y)=(-2,-6)$

Answer 1

The correct option is D $B(x,y)=(-2,-6)$

Given that:

Point $B(x,y)$ externally divides the line segment $PQ$ joining the points $P(-2,-4)$ & $Q(x_2,y_2)=(-2,-1)$ in the ratio $m:n=2:5$.

To find out- the co-ordinates of B.

Solution-

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

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

Here, $x_1=-2,x_2=-2,y_1=-4,y_2=-1,m=2,n=5.$

$\therefore x=\frac{2\times (-2)-5\times (-2)}{2-5}=-2$ and $y=\frac{2\times (-1)-5\times (-4)}{2-5}=-6$

$\therefore B(x,y)=(-2,-6)$