If the points \( \mathrm{A}\left(x_{1}, y_{1}\right), \mathrm{B}\left(x_{2}, y_{2}\right) \) and...
If the points \( \mathrm{A}\left(x_{1}, y_{1}\right), \mathrm{B}\left(x_{2}, y_{2}\right) \) and \( \mathrm{P}(h, k) \) are collinear, prove that
\[
\left(h-x_{1}\right)\left(y_{2}-y_{1}\right)=\left(k-y_{1}\right)\left(x_{2}-x_{1}\right) \text {. }
\]
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