Determining Collinear Points | A Guide in Mathematics

Collinear

In mathematics, the term “collinear” is used to describe points that lie on the same straight line

In mathematics, the term “collinear” is used to describe points that lie on the same straight line. More formally, three or more points are said to be collinear if a single straight line can pass through all of them.

To determine if points are collinear, we can visualize their positions on a coordinate plane or perform some calculations. If the three points have the same slope (rate of change) between them, then they are collinear.

For example, let’s consider three points A(2, 4), B(4, 7), and C(6, 10). To check if they are collinear, we can find the slopes between each pair of points. The slope between A and B is (7 – 4)/(4 – 2) = 3/2, and the slope between B and C is (10 – 7)/(6 – 4) = 3/2 as well. Since the slopes are equal, we conclude that the three points A, B, and C are collinear.

It is important to note that if more than two points are collinear, any two of them will have the same slope. Also, if any pair of points is collinear, all three points are collinear as well.

Knowing that points are collinear can be useful in various mathematical applications, such as geometry, trigonometry, and linear equations.

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