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Três pontos são colineares quando o determinante da matriz formada pelas coordenadas dos pontos for igual a zero.
![\left[\begin{array}{ccc} x_{1} &y_{1}&1\\x_{2}&y_{2}&1\\x_{3}&y_{3}&1\end{array}\right] \\ \\ \left[\begin{array}{ccc}3&5&1\\1&-1&1\\x&16&1\end{array}\right]=0 \\ \\ -3+5x+16+x-48-5=0 \\ \\ -40+6x=0 \\ \\ x= \frac{40}{6} \\ \\ x= \frac{20}{3}](https://tex.z-dn.net/?f=++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D+x_%7B1%7D+%26amp%3By_%7B1%7D%26amp%3B1%5C%5Cx_%7B2%7D%26amp%3By_%7B2%7D%26amp%3B1%5C%5Cx_%7B3%7D%26amp%3By_%7B3%7D%26amp%3B1%5Cend%7Barray%7D%5Cright%5D++%5C%5C++%5C%5C+++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%26amp%3B5%26amp%3B1%5C%5C1%26amp%3B-1%26amp%3B1%5C%5Cx%26amp%3B16%26amp%3B1%5Cend%7Barray%7D%5Cright%5D%3D0+%5C%5C++%5C%5C+-3%2B5x%2B16%2Bx-48-5%3D0+%5C%5C++%5C%5C+-40%2B6x%3D0+%5C%5C++%5C%5C+x%3D+%5Cfrac%7B40%7D%7B6%7D++%5C%5C++%5C%5C+x%3D+%5Cfrac%7B20%7D%7B3%7D++ "\left[\begin{array}{ccc} x_{1} &y_{1}&1\\x_{2}&y_{2}&1\\x_{3}&y_{3}&1\end{array}\right] \\ \\ \left[\begin{array}{ccc}3&5&1\\1&-1&1\\x&16&1\end{array}\right]=0 \\ \\ -3+5x+16+x-48-5=0 \\ \\ -40+6x=0 \\ \\ x= \frac{40}{6} \\ \\ x= \frac{20}{3}")
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