Define Collinear points and non-collinear points ?

Question

Answer

Collinear points are points which lie on a straight line . And non Collinear points are points which doesn't lie on a straight line.HOPE IT IS HELPFUL

Answer

The point which lies on the same line segment are called collinear points. The points lies on a same plane but doesn't on a same line segment are called non collinear points

Answer

Collinear Points and Non-Collinear Points

Collinear points are points that lie on the same straight line, while non-collinear points are points that do not lie on the same straight line. In geometry, understanding the difference between collinear and non-collinear points is crucial in various mathematical problems and constructions.

Collinear Points:
Collinear points are points that can be connected in a straight line. They lie on the same line and share a common direction. It is important to note that a minimum of two points is required to define a line, and any additional points that lie on that line are considered collinear.

Non-Collinear Points:
Non-collinear points are points that do not lie on the same line. These points may be scattered in different directions and are not connected by a straight line. In other words, no line can be drawn through non-collinear points.

Example:
To better understand collinear and non-collinear points, let's consider an example. Suppose we have three points A, B, and C. If all three points lie on the same line, they are collinear. However, if they are not on the same line, they are non-collinear.

Construction:
Collinear points can be easily constructed by drawing a straight line and marking the points on it. However, non-collinear points cannot be constructed on a single line. They may be placed randomly in different locations.

Visual Representation:
To visually represent collinear and non-collinear points, consider a line segment AB. If additional points, such as C and D, lie on the line segment AB, they are collinear. On the other hand, if points C and D are placed randomly such that they do not lie on the line segment AB, they are non-collinear.

Importance:
Understanding collinear and non-collinear points is essential in various geometric concepts and calculations. It helps in identifying and defining lines, angles, and shapes. Additionally, the concept of collinearity is used in determining whether points lie on the same line or if a line passes through a given set of points.

In conclusion, collinear points are points that lie on the same line, while non-collinear points do not lie on the same line. Recognizing and differentiating between these points is fundamental in geometry and aids in various mathematical constructions and problem-solving.

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