Question

The coordinate of the point dividing internally the line joining the points $(4,-2)$ and $(8,6)$ in the ratio $7:5$ is

• A. (16, 18)
• B. (18, 16)
• C. $\left(\frac{19}{3},\frac{8}{3}\right)$
• D. $\left(\frac{8}{3},\frac{19}{3}\right)$
• E. $(7,3)$

Answer 1

Answer: (C)

Here, $x_1=4,y_1=-2,x_2=8,y_2=6$ and $m:n=7:5$
$\therefore x=\frac{m{x}_2+n{x}_1}{m+n}=\frac{7\times 8+5\times 4}{12}$
$=\frac{56+20}{12}=\frac{76}{12}=\frac{19}{3}$
and $y=\frac{m{y}_2+n{y}_1}{m+n}$
$=\frac{7\times 6+5\times (-2)}{7+5}$
$=\frac{42-10}{12}=\frac{32}{12}=\frac{8}{3}$
$\therefore (x,y)=\left(\frac{19}{3},\frac{8}{3}\right)$