Identify the Collinear and Non-collinear point from the below figure. If we draw a line passing through two points P, Q and R , then there are two possibilities. Answer: To find the slope, you have to divide the difference of y-coordinates of 2 end-points on a line by the difference of x-coordinates of the same endpoints. With three points A, B and C, three pairs of points can be formed, they are: AB, BC and AC. Points on the cartesian plane are called ordered pairs written as (x , y). Vedantu academic counsellor will be calling you shortly for your Online Counselling session. Suppose, X, Y and Z are the three points, with which we can form three sets of pairs, such that, XY, YZ and XZ are three pairs of points. Non-Collinear Points: The points which do not lie on the same line are called non-collinear points. As slope of AB = slope of BC. And points D, E and F are non-collinear points in a plane. The word 'collinear' is the combined word of two Latin names ‘col’ + ‘linear’. Solution: If the three points P(2, 4), Q(4, 6) and R(6, 8) are collinear, then slopes of any two pairs of points, PQ, QR & PR will be equal. Suppose, X, Y and Z are the three points, with which we can form three sets of pairs, such that, XY, YZ and XZ are three pairs of points. Solution: Points A, B and C are collinear. Suppose A(x1 y1) and B(x2 y2) then their slope will be. If . If two or more than two points lie on a line close to or far from each other, then they are said to be collinear, in Euclidean geometry. Required fields are marked *. The remaining points are said to be non-collinear, i.e. Pro Lite, Vedantu Three points are collinear, if the slope of any two pairs of points is the same. Slope of AB = slope of BC = slope of AC, then A, B and C are collinear points. 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From the above figure, the slope of the straight line joining the points A (x1, y1) and B (x2, y2) is, change in y coordinates / change in x coordinates, If the general equation of a straight line is given as, then, the formula for the slope of the line is. In more astonishing observation, the term collinear has been used for straightened things, that means, something being “in a row” or “in a line”. Then, as per the slope formula. 'Co' indicates togetherness, as in coworker or cooperate. Collinear points are the points that lie on the same line. Prove that the three points R(2, 4), S (4, 6) and T(6, 8) are Collinear. Use slope formula to find the slopes of the respective pairs of points: Since slopes of any two pairs out of three pairs of points are the same, this proves that R, S and T are collinear points. There are two methods to find whether the three points are collinear or not they are: The other is the Area of Triangle method. Note: Slope of the line segment joining two points say (x1, y1) and (x2, y2) is given by the formula: Example: Show that the three points P(2, 4), Q(4, 6) and R(6, 8) are collinear. For more maths articles, visit byjus.com and download BYJU’S – The Learning App for exciting learning videos. Substitute the coordinates of the given three points in the area of triangle formula.