Day 148: Determinants to Find Area, Really?!
Today we looked at how determinants of matrices can actually be of use beyond solving matrix equations. One interesting application is using the determinant of 3 points to find the area of any coordinatized triangle. You can see the two examples we did to use the formula. It was a great way to review the process of finding the determinant of a 3×3 matrix.
However, my students wanted to know WHY this process worked. I was so thrilled with their question and so I gave them a couple of days to think about the “why” of the method. After a night of thinking, we began to explore the problem. I simply scribed for the class as they thought through the relationship. It is a nice way to connect geometry and algebra in an interesting and unexpected way!