Question

Write the formula for the area of the triangle having its vertices at (x₁, y₁), (x2, y₂) and (x₃, y₃).

Answer 1

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 )|`