Question
Find the area of the triangle formed by the points A(1,
2), B(4, 6), and C(5, 1).Solution
To find the area of a triangle formed by three points (x1, y1), (x2, y2), and (x3, y3), we use the formula: Area = (1/2) | x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2) | Substituting the coordinates of points A, B, and C: x1 = 1, y1 = 2 x2 = 4, y2 = 6 x3 = 5, y3 = 1 Area = (1/2) | 1(6 - 1) + 4(1 - 2) + 5(2 - 6) | = (1/2) | 1(5) + 4(-1) + 5(-4) | = (1/2) | 5 - 4 - 20 | = (1/2) | 5 - 24 | = (1/2) | -19 | = (1/2) × 19 = 9.5 Thus, the area of the triangle is: 9.5 Correct Answer: c
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