collinear
points that lie on the same line
Collinear refers to a set of points that lie on a single straight line. In other words, if three or more points lie on a line, they are said to be collinear. This concept is important in geometry and is used in many mathematical and scientific applications.
To determine if a set of points are collinear, we can use the collinear points theorem. This theorem states that if three points are collinear, then the slope between any two of them is equal. We can use this theorem to check if a set of points are collinear by calculating the slope between each pair of points and verifying that the slopes are equal.
For example, if we have three points A(x1, y1), B(x2, y2), and C(x3, y3), we can use the slope formula to calculate the slope between A and B, B and C, and A and C. If the slopes between all three pairs are equal, then the points are collinear.
Collinear points are commonly used in applications such as designing buildings, bridges, and roadways. Understanding the concept of collinearity helps engineers and architects determine the position and orientation of structures, ensuring that they are safe and stable.
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