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} $
$\therefore (x, y) =\left(\frac{19}{3}, \frac{8}{3}\right)$