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Question
Find the area of a triangle with vertices at the point given in the following:
(2, 7), (1, 1), (10, 8)
Solution
Area of a triangle known from vertex units `(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))`
Area of the required triangle
`Delta = 1/2 abs ((2,7,1),(1,1,1),(10,8,1))`
`= 1/2 [2 (1 - 8) - 7 (1 - 10) + 8 (8 - 10)]`
`= 1/2 [-16 + 63]`
`= 47/2`
= 23.5 sq.units
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