If the area of the triangle formed by $(- 2, 5), (x, - 3)$ and $(3, 2)$ is $14$ square units, then $x =$ ____.

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Solution

The correct option is B 2
Area of triangle having vertices $(x_{1}, y_{1}), (x_{2}, y_{2})$ and $(x_{3}, y_{3})$ is given by
$= \frac{1}{2} \times [x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})]$
$∴ A r e a = \frac{1}{2} [- 2 (- 3 - 2) + x (2 - 5) + 3 (5 + 3)]$
$= \frac{1}{2} [10 - 3 x + 24] = \frac{34 - 3 x}{2}$
$∴ \frac{34 - 3 x}{2} = 14$ or x = 2

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