Write condition of collinearity of three points $A (x_{1}, x_{2}), B (x_{2}, y_{2})$ and $C (x_{3}, y_{3})$

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Solution

$\begin{matrix} A (x_{1}, x_{2}), B (x_{2}, y_{2}), C (x_{3}, y_{3}) \Rightarrow s l o p e o f A B = s l o p e B C i f a r e a o f t r i a n g l e i s z e r o t h e n, p o i n t s a r e i n c o l l i n e a r \Rightarrow \frac{1}{2} [x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})] = 0 \end{matrix}$

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