Determining Collinearity | Methods and Concepts in Mathematics

Collinear

In mathematics, the term “collinear” refers to a set of points that lie on the same straight line

In mathematics, the term “collinear” refers to a set of points that lie on the same straight line. If three or more points are collinear, there exists a single line that passes through all of them. This means that the points are aligned in a linear fashion and can be connected with a straight line.

To determine if a set of points is collinear, you can follow a few methods:

1. Visual inspection: If you are given a set of points on a coordinate plane or in a geometric figure, you can visually analyze if they lie on the same straight line. If you can draw a straight line passing through all of them, the points are collinear.

2. Slope calculation: If you have the coordinates of three points, you can use the slope formula to check if they are collinear. The slope of the line passing through two points, say (x1, y1) and (x2, y2), is given by (y2 – y1) / (x2 – x1). If the slopes between all pairs of points are equal, then the points are collinear.

3. Area calculation: Alternatively, you can calculate the area of the triangle formed by three non-collinear points. If the area is zero, it means that the points are collinear.

It is important to note that collinearity is a concept that can be extended to higher dimensions as well. In three-dimensional space, for instance, four or more points can be collinear if they lie on the same straight line.

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