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Question
Find the area of a triangle with vertices at the point given in the following:
(−2, −3), (3, 2), (−1, −8)
Solution
Area of the triangle passing through the vertices `(x_1,y_1),(x_2,y_2),(x_3,y_3)`,
`Delta = 1/2 abs ((x_1,y_1,1),(x_2,y_2,1),(x_3,y_3,1))`
`Delta = 1/2 abs ((-2,-3,1),(3,2,1),(-1,-8,1))`
`= 1/2 [-2 ( 2 + 8) + 3 (3 + 1) + (-24 + 2)]`
`= 1/2 [-2 (10) + 3 (4) + (- 22)]`
`= 1/2 [-20 + 12 - 22]`
`= - 30/2`
= - 15
∴ Area = 15 square units. (As area > 0)
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