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Question
The area of a triangle with vertices at (−4, −1), (1, 2) and (4, −3) is
Options
17
16
15
none of these
Solution
17
Let A be the area of the triangle formed by the points (−4, −1), (1, 2) and (4, −3).
\[\therefore A = \frac{1}{2}\left| \left\{ x_1 \left( y_2 - y_3 \right) + x_2 \left( y_3 - y_1 \right) + x_3 \left( y_1 - y_2 \right) \right\} \right|\]
\[ \Rightarrow A = \frac{1}{2}\left| \left\{ - 4\left( 2 + 3 \right) + 1\left( - 3 + 1 \right) + 4\left( - 1 - 2 \right) \right\} \right|\]
\[ \Rightarrow A = 17\]
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