Question

What is the formula for area of triangle when given three coordinates?

Answer 1

Let the given coordinates be A(x₁, y₁), B(x₂, y₂) and C(x₃, y₃).

   It is simpler to do calculations and to remember the formula, if we translate the origin to vertex A.

So new coordinates will be as:  (with A as the origin)
         A' = (0, 0),    B' = (X₂, Y₂)  ,   C' = (X₃, Y₃)
 
               where  X₂ = x₂ - x₁ ,   Y₂ = y₂ - y₁
                           X₃ = x₃ - x₁,    Y₃ = y₃ - y₁

The formula for  ar(ΔABC) = 1/2 * | X₃ Y₂ - X₂ Y₃ |

This is an extremely simple formula and easy to calculate too.