Using determinants, find equation of line passing through $(- 3, 4)$ and $(1, 5)$ .

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Solution

We know that
$\begin{matrix} ⎛ ⎜ ⎝ \begin{matrix} x & y & 1 x_{1} & y_{1} & 1 x_{2} & y_{2} & 1 \end{matrix} ⎞ ⎟ ⎠ = 0 p o i n t i s (\begin{matrix} x_{1} & y_{1} - 3 & 4 \end{matrix}) a n d (\begin{matrix} x_{2} & y_{2} 1 & 5 \end{matrix}) ⎛ ⎜ ⎝ \begin{matrix} x & y & 1 - 3 & 4 & 1 1 & 5 & 1 \end{matrix} ⎞ ⎟ ⎠ = 0 x (4 - 5) - y (- 3 - 1) + 1 (- 15 - 4) = 0 - x + 4 y - 19 = 0 x - 4 y + 19 = 0 \end{matrix}$

Hence, this is the answer.

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