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I have a basic grasp of matrices and I was just wondering to which transformation does this matrix correspond? $$A = \begin{bmatrix}x_1 & y_1 & 1 \\ x_2 & y_2 & 1 \\ x_3 & y_3 & 1\end{bmatrix}$$

It is used for calculating the area of a triangle with three known vertices as, $Area= \frac{1}{2}\det{A}$. Why are we transforming each basis vector to the $z=1$ plane?

KReiser
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Utkarsh Verma
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  • Related questions (which explain the formula, although I don't know if they answer your specific question about an interpretation): https://math.stackexchange.com/questions/299352/show-that-the-area-of-a-triangle-is-given-by-this-determinant, https://math.stackexchange.com/questions/516219/finding-out-the-area-of-a-triangle-if-the-coordinates-of-the-three-vertices-are – Hans Lundmark Oct 25 '18 at 08:16
  • @HansLundmark They are similar but don't answer my question which focuses on intuition rather than proofs. – Utkarsh Verma Oct 25 '18 at 15:18

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