Question

Three points are collinear.

Answer 1

If they are in the same line yes. If they aren't then its considered non-collinear.

Answer 2

Three points are collinear if they belong to the same line. Also if their Determinant equals zero.

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.

`\left[\begin{array}{ccc}x&y&1\\&&1\\&&1\end{array}\right]`

Applying:

Det=
`\left[\begin{array}{ccc}-6&2&1\\-3&-1&1\\-5&1&1\end{array}\right]`=0

Doing the calculation, the Determinant equals zero, what gives us an Analytical Geometry proof of its collinearity.