Question

The co-ordinate of the point dividing internally the line joining the points (4, –2) and (8, 6) in the ratio 7: 5 will be

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

Answer 1

Answer: (C)

$\left( \frac{19}{3},\frac{8}{3} \right)$

Answer 2

Let point (x, y) divides the line internally.

Then $x = \frac{m_{1}x_{2} + m_{2}x_{1}}{m_{1} + m_{2}}$=$\frac{7(8) + 5(4)}{12} = \frac{19}{3}$, $y = \frac{m_{1}y_{2} + m_{2}y_{1}}{m_{1} + m_{2}}$

=$\frac{7(6) + 5( - 2)}{12} = \frac{8}{3}$

Then $x = \frac{m_{1}x_{2} + m_{2}x_{1}}{m_{1} + m_{2}}$=$\frac{7(8) + 5(4)}{12} = \frac{19}{3}$, $y = \frac{m_{1}y_{2} + m_{2}y_{1}}{m_{1} + m_{2}}$

=$\frac{7(6) + 5( - 2)}{12} = \frac{8}{3}$