If the points A(x,y), B(3, 6) and C(−3,4) are collinear,show that x − 3y + 15 = 0

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Solution

Since, the points A(x,y), B(3, 6) and C(−3,4) are collinear
Hence, the area of traiangle is zero.
$\Rightarrow \frac{1}{2} [x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})] = 0 \Rightarrow x (6 - 4) + 3 (4 - y) - 3 (y - 6) = 0 \Rightarrow 2 x + 12 - 3 y - 3 y + 18 = 0 \Rightarrow 2 x - 6 y + 30 = 0 \Rightarrow x - 3 y + 15 = 0$

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