Area of triangle using determinants

In a 2D plane,

For three points

   A (x ₁ , y ₁ ),

  B (x ₂ , y ₂ ),

  C (x ₃ , y ₃ )

Find area of triangle with vertices (3, 8), (-4, 2), (5, 1)

Check solution - Example 17

Important Points

There are some points to note:-

1. If Area of triangle = 0 ,
   then the three points are collinear
   
   
2. If the value of determinant comes negative, we will take the
   positive value as area
   
   

   Example
   

   
   
   
   Therefore,
   Area = 45 square units
   
   

3. If area is given,
   We take both positive and negative value of determinant
   Example
   If Area = 3 square units

Check the questions below to learn more