The area of the triangle formed by any three collinear points will always be zero. If three points are collinear, the slopes formed from any two points are the same as the slope formed by the other two. There are three main ways of finding whether points are collinear or not. Points that are positioned at non-linear positions on which a straight line cannot be formed are known as non-linear points. Three or more points lying on the same straight line are known as the collinear points. But more than 3 points are usually NOT on the one plane (unless they are carefully chosen to be). 3 points are always coplanar because you can have a plane that they are all on. (x1, y1) => (4, 4) and (x2, y2) => (-2, 6) Definition of Coplanar Lying on a common plane. Ques: Prove that the given three points (4, 4), (-2, 6), and (1, 5) are collinear points using Slope Formula Method. This proves that given three points A, B, and C are collinear. To find the lengths AB, BC and AC using the formula, Ques: Prove that points A(5, -2), B(4, -1) and C(1, 2) are collinear points using the Distance Method.ĭistance between any two points (x1, y1) and (x2, y2) is Points that are not on the same line and through which a straight line can never be formed, are known as non-collinear points.įor Example, Let consider the following figure, we cannot draw lines combining the points P, Q, R, S & T. Now, by the distance formula we know, the distance between two points (x1, y1) and (x2, y2) is given by 
If the distance between the 1st point and 2nd point added to the distance between 2nd point and 3rd point is equal to the distance between 1st and 3rd point, then all the three points are collinear.įor example, If we take A, B, and C as any three collinear points, then,ĭistance from A to B + Distance from B to C = Distance from A to C (1/2) | | = 0Īlso Read: Lines and Angles MCQs Distance Method If the area is 0, the points are collinear.įor Example, The three points A(x1, y1), B(x2, y2), and C(x3, 圓) are collinear, then by remembering the formula of area of the triangle formed by three points we get
So, if Slope of AB= Slope of BC, then A, B, and C are collinear points.Īlso Read: Three Dimensional Geometry Area of the Triangle MethodĪnother method to prove whether the points are collinear points or not is by finding the area of the triangle formed by the three points. If the slope of any two pairs of points is the same, then the three points are definitely on the same line and they are collinear.įor example, Imagine there are three points- A, B, and C. There are three basic ways of finding if three points are collinear or not. Important Concepts Related to Collinear Points
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