Question

If the line joining points $(5,-6)$ and $(9,8)$ divided by a point R internally in $5:6$ ratio, then R =

• A. ($\frac{5}{11},\frac{4}{11}$)
• B. ($\frac{75}{11},\frac{76}{11}$)
• C. ($\frac{75}{11},\frac{4}{11}$)
• D. None of these

Answer 1

The correct option is C ($\frac{75}{11},\frac{4}{11}$)

The given points are $A=(x_1,y_1)=(5,-6),B=(x_2,y_2)=(9,8)$

Now, $R=(X,Y)$ divides the line segment AB internally in the ratio $m:n=5:6$.

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

$\therefore X=\frac{5\times 9+6\times 5}{5+6}=\frac{75}{11}$ and $Y=\frac{5\times 8+6\times (-6)}{5+6}=\frac{4}{11}$

Therefore, given point $R$ is $(\frac{75}{11},\frac{4}{11})$.