Determining Collinear Points using Slope: A Mathematical Explanation

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, three or more points are said to be collinear if they can all be connected by a single straight line.

To determine if three points are collinear, you can use the concept of slope. The slope of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula:

slope = (y2 – y1) / (x2 – x1)

If three points (x1, y1), (x2, y2), and (x3, y3) are collinear, then the slopes of the lines formed by connecting any two of these points must be equal.

For example, let’s consider three points A(2, 3), B(5, 7), and C(8, 11). We can calculate the slopes of the lines AB and BC to determine if these points are collinear.

Slope of AB:
m_AB = (y2 – y1) / (x2 – x1)
= (7 – 3) / (5 – 2)
= 4 / 3

Slope of BC:
m_BC = (y3 – y2) / (x3 – x2)
= (11 – 7) / (8 – 5)
= 4 / 3

Since the slopes of lines AB and BC are equal, we can conclude that points A, B, and C are collinear.

It is important to note that while the concept of collinear points is applicable to any number of points, the example above demonstrates its application with three points.

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