The ratio in which $(2, 1)$ divides the line segment joining $(1, 4), (4, - 5)$ is

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$1 : 3$

$1 : 2$

$2 : 3$

$4 : 5$

answer is A.

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Detailed Solution

$\begin{array}{l} L e t P (x, y) = (2, 1), A (x_{1}, y_{1}) = (1, 4) a n d B (x_{2}, y_{2}) = (4, - 5) \\ The required ratio x_{1} - x : x - x_{2} or y_{1} - y : y - y_{2} \\ 1 - 2 : 2 - 4 \\ - 1 : - 2 \\ 1 : 2 \end{array}$

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