What does collinear mean?
http://mathworld.wolfram.com/Collinear.html
"Collinear" is a geometric term used to describe points or objects that lie on the same straight line. When three or more points are collinear, it means that they can all be connected by a single straight line. The term "co-" means together, and "linear" refers to a line. So, collinear points are points that belong to the same line.
To determine if given points are collinear, you can use the concept of slope. The slope is the measure of how steep a line is. If the slopes between any two pairs of points are equal, then the points are collinear. You can calculate the slope using the formula: slope = (change in y)/(change in x). If the slopes of all pairs of points are equal, then the points are collinear.
Another method is to use the concept of vectors. If you can express the displacement vectors between any two points using scalar multiples of each other, then the points are collinear. For example, if the displacement vector from point A to point B is 2 times the displacement vector from point B to point C, the points A, B, and C are collinear.
These methods can help you determine if a set of points on a plane are collinear or not.