Question
Find the area of the triangle formed by the points A(2, 3), B(-1, -4), and C(5, -2).
Solution
The area of a triangle with vertices (x1, y1), (x2, y2), and (x3, y3) is given by: Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|. Substituting the given points: Area = 1/2 * |2(-4 - (-2)) + (-1)(-2 - 3) + 5(3 - (-4))| = 1/2 * |2(-2) + (-1)(-5) + 5(7)| = 1/2 * |-4 + 5 + 35| = 1/2 * |36| = 18 square units.
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