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Question
Write the formula for the area of the triangle having its vertices at (x1, y1), (x2, y2) and (x3, y3).
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Solution
The formula for the area ‘A’ encompassed by three points
`(x_1 , y_1 ) , (x_2 , y_2) " and " (x_3 , x_3)` is given by the formula,
`A = 1/2 | [x_1 - x_2 y_1 - y_ 2 ] , [ x_2 - x_3 y_2 - y_ 3] |`
`A = 1/2 |(x_1 - x_2 )(y_2 - y_3 )-(x_2 -x_3)(y_1 - y_2)|`
The area ‘A’ encompassed by three points `(x_1 , y_1 ) , (x_2 , y_2) " and " (x_3 , x_3)` is also given by the formula,
`A = 1/2 |x_1 (y_2 - y_3) + x_2 (y_3 - y_1 ) + x_3 (y_1 - y_2 )|`
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