Answer:
Three points are collinear if they belong to the same line. Also if their Determinant equals zero.
Step-by-step explanation:
Suppose we have A (-6, 2) B(-3,-1) and D(-5, 1). Are they collinear?
Well, let's plug in the values in a Matrix and then calculate its Determinant this way:
Plug ig the values for x, y and complete it with 1 in the 3rd column.
[tex]\left[\begin{array}{ccc}x&y&1\\&&1\\&&1\end{array}\right][/tex]
Applying:
Det=[tex]\left[\begin{array}{ccc}-6&2&1\\-3&-1&1\\-5&1&1\end{array}\right][/tex]=0
Doing the calculation, the Determinant equals zero, what gives us an Analytical Geometry proof of its collinearity.
