How do you find areas of triangle using determinants?

Answer 1

Let the 3 vertices of the triangle be 3 points. Each point is an ordered pair. Write the 3 points as rows of a 3x3 matrix with each point being a row and the third entry in each row is 1. For example if one vertex was located at (1,2) The row of the matrix would be 1 2 1

Do the same with all the vertices.

Then take 1/2 the determinant of that matrix and that is the area. If it is a negative number, then take the positive value. It will be negative or positive depending on the order of the rows, but area is always positive.