Collinear points Chapter 1 (p. 4)
In mathematics, collinear points are points that lie on the same straight line
In mathematics, collinear points are points that lie on the same straight line. More specifically, three or more points are said to be collinear if they lie on the same line. This line on which the points lie is called the line of collinearity.
To determine if three points are collinear, you can use the concept of slope. If the slope between any two pairs of points is equal, then the three points are collinear. Another method to check for collinearity is to calculate the area of the triangle formed by the three points. If the area is zero, then the points are collinear.
For example, if you have three points A, B, and C, you can check if they are collinear as follows:
1. Method 1: Slope
Calculate the slopes between AB, AC, and BC. If all three slopes are equal, then the points A, B, and C are collinear.
2. Method 2: Area
Calculate the area of triangle ABC. If the area is zero, then the points A, B, and C are collinear.
It is important to note that any two points are always collinear since they can be connected by a straight line. However, when speaking specifically about collinear points, we are referring to three or more points lying on the same line.
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