Understanding Collinear Points and Calculating Slopes – A Guide to Determining Collinearity in Mathematics

collinear points

Collinear points are points that lie on the same line

Collinear points are points that lie on the same line. In other words, if you have three or more points that are collinear, you can draw a straight line that passes through all of them.

Collinearity can be easily determined by examining the slopes of the lines that connect the points. If the slopes of all the lines are the same, then the points are collinear.

Let’s say we have three points: A(x1, y1), B(x2, y2), and C(x3, y3). To check for collinearity, we’ll calculate the slopes of the lines AB and BC. If the slopes are equal, then these points are collinear.

The formula for calculating the slope (m) of a line passing through two points (x1, y1) and (x2, y2) is:

m = (y2 – y1) / (x2 – x1)

Let’s calculate the slopes for the lines AB and BC:

AB slope = (y2 – y1) / (x2 – x1)
BC slope = (y3 – y2) / (x3 – x2)

If AB slope is equal to BC slope, then points A, B, and C are collinear.

For example, let’s consider the points A(1, 2), B(3, 4), and C(5, 6):

AB slope = (4 – 2) / (3 – 1) = 2 / 2 = 1
BC slope = (6 – 4) / (5 – 3) = 2 / 2 = 1

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

In summary, collinear points are points that lie on the same line. To determine if points are collinear, calculate the slopes of the lines connecting the points. If the slopes are equal, the points are collinear.

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