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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).
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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