In which ratio $P (2 a - 2, 4 a - 6))$ divided $Q (2 a - 3, 3 a - 7)$ and $R (2 a, 6 a - 4) .$

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Solution

We know that by section formula, the co-ordinates of the points which divide internally the line segment joining the points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ in the ratio $m : n$ is
$(x, y) = (\frac{m x_{2} + n x_{1}}{m + n}, \frac{m y_{2} + n y_{1}}{m + n})$
Let the ratio in which P cuts QR be $m : n$
=> $(2 a - 2, 4 a - 6) = (\frac{(2 a - 3) n + m (2 a)}{m + n}, \frac{(3 a - 7) n + m (6 a - 4)}{m + n}) => 2 a m - 2 m + 2 a n - 2 n = 2 a n - 3 n + 2 a m => 2 m = n => m : n = 1 : 2$

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