Determining Collinearity of Points | Test and Calculation Examples

collinear points

Collinear points are points that lie on the same straight line

Collinear points are points that lie on the same straight line. In other words, if you can draw a line through two or more points, they are said to be collinear.

To determine if three points are collinear, you can use the collinearity test. A simple way to perform this test is by calculating the slope between the first two points and then checking if the slope between the second and third points is the same. If the slopes are equal, it means the three points lie on the same line and are collinear. However, if the slopes are different, the points are not collinear.

For example, let’s consider three points: A(3, 4), B(5, 6), and C(7, 8). To check their collinearity, we can calculate the slopes:

Slope between A and B:
m₁ = (y₂ – y₁) / (x₂ – x₁)
m₁ = (6 – 4) / (5 – 3) = 2/2 = 1

Slope between B and C:
m₂ = (y₃ – y₂) / (x₃ – x₂)
m₂ = (8 – 6) / (7 – 5) = 2/2 = 1

Since the slopes are equal (m₁ = m₂ = 1), the points A, B, and C are collinear, as they lie on the same line.

Collinear points have a useful property called the “betweenness of points.” This property states that if three points A, B, and C are collinear and point B is between A and C, then the distance between A and B plus the distance between B and C will equal the distance between A and C.

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