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Someone2841
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Collinear means, etymologically, "in line with". Essentially, if you can draw a strait line through any number of points, those points are deemed to be collinear.
Any two points are collinear (i.e., you can draw a strait line through any two points), but three or more points may not be.
Let's take an example. three points\(\displaystyle (x,y)\) are \(\displaystyle (0,0), (2,2), (5,5)\). Are these points collinear? Let's form an equation for a line through the first two.
\(\displaystyle m = \frac{2-0}{2-0} = 1\)
With the point slope formula using \(\displaystyle (0,0)\) we get:
\(\displaystyle y - 0 = m(x - 0) \to y = x\)
If point \(\displaystyle (5,5)\) is a solution to this equation, then it is on the same line as \(\displaystyle (0,0)\) and \(\displaystyle (2,2)\). Let's check:
\(\displaystyle 5 = 5\)
Because \(\displaystyle (5,5)\) is a solution to the equation for the line going through \(\displaystyle (0,0)\) and \(\displaystyle (2,2)\), all three of these points are considered collinear.
