Question

The co-ordinates of the point B which divides segment PQ joining the points $P(-2,-4)$ and $Q(-2,-1)$ externally in the ratio $m:n=7:1$ are

• A. $B(x,y)=(2,-\frac{1}{2})$
• B. $B(x,y)=(-2,\frac{1}{2})$
• C. $B(x,y)=(-2,-\frac{1}{2})$
• D. $B(x,y)=(2,\frac{1}{2})$

Answer 1

Answer: (C)

$B(x,y)=(-2,-\frac{1}{2})$

Given that- the 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 $m:n=7:1$

To find out- the coordinates 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 $x_1=-2,x_2=-2,y_1=-4,y_2=-1,m=7,n=1$

$\therefore x=\frac{7\times (-2)-1\times (-2)}{7-1}=-2$

And $y=\frac{7\times (-1)-1\times (-4)}{7-1}=-\frac{1}{2}$

$\therefore B(x,y)=(-2,-\frac{1}{2})$