# Using a determinant to find the area of the triangle (deriving the formula)

## Homework Statement:

Shown in the text

## Relevant Equations:

Det(A) = det(A^T) determinant of transpose equals determinant of the original matrix

This is the question. The following is the solutions I found:

I understand that the first line was derived by setting one vertex on origin and taking the transpose of the matrix. However, I cannot understand where the extra row and column came from in the second line. Can anyone explain how the formula is derived?

Thank you!

Related Calculus and Beyond Homework Help News on Phys.org
Math_QED
$$\det \begin{pmatrix}a & b & 1 \\ c & d & 0 \\ e & f & 0\end{pmatrix}= \det \begin{pmatrix} c & d \\ e & f\end{pmatrix}$$