collinear
In mathematics, points that lie on the same straight line are described as collinear
In mathematics, points that lie on the same straight line are described as collinear. In other words, if three or more points are collinear, it means they can all be connected by a single straight line.
To determine if points are collinear, we can use the slope-intercept form of a linear equation. Suppose we have three points A(x₁, y₁), B(x₂, y₂), and C(x₃, y₃). We can find the slope of the line formed by points A and B using the formula:
slope_AB = (y₂ – y₁) / (x₂ – x₁)
Similarly, we can find the slope of the line formed by points A and C:
slope_AC = (y₃ – y₁) / (x₃ – x₁)
If these two slopes are equal, then the three points are collinear. This is because the slopes represent the rate of change of y with respect to x for the line passing through the two respective points.
To illustrate this with an example, let’s consider three points A(2, 4), B(4, 8), and C(6, 12).
slope_AB = (8 – 4) / (4 – 2) = 4 / 2 = 2
slope_AC = (12 – 4) / (6 – 2) = 8 / 4 = 2
Since the slopes of AB and AC are equal, we conclude that points A, B, and C are collinear.
It is worth noting that the concept of collinearity extends beyond three points. Any number of points that can be connected by a straight line are considered collinear. So, if you have more than three points, you can check for collinearity by computing the slope between adjacent pairs of points and verifying if they are all equal. If they are, then all the points are collinear.
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