Find the co-ordinates of the point which divides the line joining
Question.

Find the co-ordinates of the point which divides the line joining of (–1, 7) and (4, –3) in the ratio 2 : 3.

Solution:

Let the required point be P(x, y).

Here the end points are (–1, 7) and (4, –3)

$\because \quad$ Ratio $=2: 3=\mathrm{m}_{1}: \mathrm{m}_{2}$

$\therefore \quad x=\frac{m_{1} x_{2}+m_{2} x_{1}}{m_{1}+m_{2}}=\frac{(2 \times 4)+3(-1)}{2+3}$

$=\frac{8-3}{5}=\frac{5}{5}=1$

And $y=\frac{m_{1} y_{2}+m_{2} y_{1}}{m_{1}+m_{2}}$

$=\frac{2 \times(-3)+(3 \times 7)}{2+3}=\frac{-6+21}{5}=\frac{15}{5}=3$

Thus, the required point is $(1,3)$.
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