Find the ratio in which $(- 3, 4)$ divides the line joining $(1, 2)$ and $(7, - 1)$

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Solution

Using Section Formula,
Taking the ratio as $k : 1$ in which the point $P$ divides, we have the co-ordinates to be $[\frac{k x_{2} + x_{1}}{k + 1}, \frac{k y_{2} + y_{1}}{k + 1}]$

$\frac{7 k + 1}{k + 1} = - 3 \Rightarrow \frac{k}{1} = - \frac{2}{5}$
i.e., 2 : 5 externally

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The point which divides the join of $(1, 2)$ and $(3, 4)$ externally in the ratio 1 : 1

3 x + 4 y = 7

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(4, 2, 1)

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