Question

The co-ordinates of a point $R$ which divides the line joining $A(-3,3)$ and $B(2,-7)$ internally in the ratio $2:3$ are

• A. $(1,1)$
• B. $(-1,-1)$
• C. $(2,2)$
• D. $(3,3)$

Answer 1

The correct option is B $(-1,-1)$

The given points are $A=(x_1,y_1)=(-3,3),B=(x_2,y_2)=(2,-7)$

Now, $R=(X,Y)$ divides the line segment AB internally in the ratio $m:n=2:3$.

We know $X=\frac{m{x}_2+n{x}_1}{m+n}$ and $Y=\frac{m{y}_2+n{y}_1}{m+n}$

$\therefore X=\frac{2\times 2+3\times (-3)}{2+3}=-\frac{5}{5}=-1$ and $Y=\frac{2\times (-7)+3\times 3}{2+3}=-\frac{5}{5}=-1$

$\therefore (X,Y)=(-1,-1)$