## Determinants

# Area of a Triangle

- The area of a triangle whose vertices are (x
_{1}, y_{1}), (x_{2}, y_{2}) and (x_{3}, y_{3}), is given by

\Delta=\frac{1}{2}\begin{vmatrix}x_{1} & y_{1} & 1 \\x_{2} & y_{2} & 1 \\x_{3} & y_{3} & 1 \end{vmatrix}

- Since area is a positive quantity, we always take the absolute value of the determinant.
- If area is given, use both positive and negative values of the determinant for calculation.
- The area of the triangle formed by three collinear points is zero.

### View the Topic in this video From 00:15 To 06:01

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1. The area of a triangle whose vertices are (x_{1}, y_{1}), (x_{2}, y_{2}) and (x_{3}, y_{3}), is given by

\Delta=\frac{1}{2}\begin{vmatrix}x_{1} & y_{1} & 1 \\x_{2} & y_{2} & 1 \\x_{3} & y_{3} & 1 \end{vmatrix}