If the points $(x, y), (- 5, - 2)$ and $(3, - 5)$ are collinear, then prove that $3 x + 8 y + 31 = 0$ .

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Solution

If $(x, y)$ $(- 5, - 2)$ $a n d$ (3,-5)$ are collinear.
The area bounded by them= $0$
=> $\frac{1}{2} ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} x & y - 5 & - 2 3 & - 5 x & y \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ = 0 => - 2 x + 5 y + 31 + 3 y + 5 x = 0 => 3 x + 8 y + 31 = 0$

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