Question

find the point which divides the line segment joining the points (3,5), and (8,10) internally in the ratio 2:3.

Answer 1

$\frac{m_{1} }{ m_{2} } = \frac{2}{3} \\ \\ \\ \\ m_{1} = 2 \: \: \: \: \: \: \: and \: \: \: \: \: \: m_{2} = 3$





We Know,




$x = \frac{ m_{1}x _{2} + m_{2} x_{1}}{ m_{1} \: + \: m_{2} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: y \: = \frac{ m_{1}y _{2} + m_{2} y_{1}}{ m_{1} \: + \: m_{2} }$


Hence,




$x = \frac{(2 \times 8) + (3 \times 3)}{2 + 3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: y = \frac{(2 \times 10) + (3 \times 5)}{2 + 3} \\ \\ \\ x = \frac{16 + 9}{5} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: y = \frac{20 + 35}{5} \\ \\ \\x = \frac{25}{5} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: y = \frac{55}{5}$



x = 5 and y = 11





Required Point = { 5 , 11 }