Exploring Non-Collinear Points In Geometry And Trigonometry

Non-Collinear

Points that do not lie on the same line

Non-collinear refers to a set of points that do not lie on the same line. In other words, if three or more points are non-collinear, then they do not form a straight line.

For example, consider the points A(1,2), B(5,3), and C(10,8) on a two-dimensional coordinate plane. By drawing a line through any two of these points, it is clear that the three points are not collinear since a line cannot connect all three points. Therefore, A, B, and C are non-collinear points.

In three dimensions, we can think of non-collinear points as points that are not on the same plane. For example, the vertices of a triangular pyramid are non-collinear since they cannot be connected by a single flat surface.

Understanding non-collinear points is important in geometry and trigonometry as it helps us to define shapes and angles. For instance, a triangle can only be formed by three non-collinear points and the angles between the sides of the triangle can only be measured if the points are non-collinear.

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