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. Therefore, the three points P, Q and R are collinear. They are: Slope Formula; Area of triangle; Using Slope Formula: Three or more points are said to be collinear if the slope of any two pairs of points is the same. From the above definition, it is clear that the points which lie on the same line are collinear points. With three points R, S and T, three pairs of points can be formed, they are: RS, ST and RT. Required fields are marked *. Suppose A(x1 y1) and B(x2 y2) then their slope will be. If a point R does not lie on the line, then points P, Q and R do not lie on the same line and are said to be non- collinear points. With three points R, S and T, three pairs of points can be formed, they are: RS, ST and RT. Slope of AB = slope of BC = slope of AC, then A, B and C are collinear points. 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. Answer: A graph with two perpendicular number lines used to describe any point in the plane using an ordered pair of numbers is called a Cartesian Plane or the coordinate plane. Suppose, the three points P(x1, y1), Q(x2, y2) and R(x3, y3) are collinear, then by remembering the formula of area of triangle formed by three points we get; (1/2) | [x1(y2 – y3) + x2(y3 – y1) + x3[y1 – y2]| = 0. If Slope of XY = Slope of YZ = Slope of XZ, then the points X, Y and Z are collinear. Let the point be A (2, 5), B (24, 7) and C (12, 4). Using the Area of Triangle Formula: If the area of triangle formed by three points is zero, then they are said to be 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. The term collinear is the combined word of two Latin names ‘col’ + ‘linear’. Sorry!, This page is not available for now to bookmark. If we draw a line passing through two points P, Q and R , then there are two possibilities. Three points are collinear, if the slope of any two pairs of points is the same. Slope formula method to find that points are collinear. You may see many real-life examples of collinearity such as a group of students standing in a straight line, eggs in a carton are kept in a row, next to each other, etc. Using slope formula to solve this problem. The slope of the line basically measures the steepness of the line. Check whether the points (2, 5) (24, 7) and (12, 4) are Collinear or not? 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. In more astonishing observation, the term collinear has been used for straightened things, that means, something being “in a row” or “in a line”. Therefore, collinear points mean points together in a single line. Find x. In this article let us study collinear points definition and how to find collinear points? Solution: As per the area of triangle formula for three coordinates in a plane, Area = \(\frac{1}{2}\begin{vmatrix} 2-4 & 4-6 \\ 3-0 & 0+3 \end{vmatrix}\\ = \frac{1}{2}\begin{vmatrix} -2 & -2\\ 3 & 3 \end{vmatrix}\). As slope of AB = slope of BC. Since the result for the area of the triangle is zero, therefore R (2, 4), S (4, 6) and T (6, 8) are collinear points. {P, B}, {C, E} and so on. Number of lines through these three non-collinear points is 3  ([Image will be uploaded soon]), If P, Q, R & S are non- collinear points then, Number of lines through these four non-collinear points is 6 ([Image will be uploaded soon]), So in general we can say number of lines through “n” non-collinear points = \[\frac{n(n-1)}{2}\]. As given the points P, Q and R are collinear we have. If . Your email address will not be published. In a given plane, three or more points that lie on the same straight line are called collinear points. The set of points which do not lie on the same straight line are said to be non-collinear points.in the below figure points X, Y, and Z do not make a straight line so they are called as the non-collinear points in a plane. The remaining points are said to be non-collinear, i.e. 'Linear' refers to a line. The three points A, B and C are collinear, if the sum of the lengths of any two line segments among AB, BC and AC is equal to the length of the remaining line segment. Three or more points are collinear, if slope of any two pairs of points is same. If the three points R (2, 4), S (4, 6) and T (6, 8) are collinear, then slopes of any two pairs of points will be equal. There are two methods to find the collinear points. Two points are always in a straight line.In geometry, collinearity of a set of points is the property of the points lying on a single line.A set of points with this property is said to be collinear. If the A, B and C are three collinear points then AB + BC = AC or AB = AC - BC or BC = AC - AB. The word 'collinear' is the combined word of two Latin names ‘col’ + ‘linear’. Non-Collinear Points: The points which do not lie on the same line are called non-collinear points. It means that if three points are collinear, then they cannot form a triangle. Formula for area of a triangle formed by three points is, \[\frac{1}{2}\begin{vmatrix}x_1-x_2&x_2-x_3 \\ y_1-y_2&y_2-y_3 \end{vmatrix}\]. We can say that the given points A (2, 5), B (24, 7) and C (12, 4) are collinear. Slope of AB = \[\frac{y_2-y_1}{x_2-x_1}\]= \[\frac{7-5}{10-2}\]= \[\frac{2}{8}\]=  \[\frac{1}{4}\], Slope of BC = \[\frac{y_2-y_1}{x_2-x_1}\]= \[\frac{4-7}{12-24}\]= \[\frac{-3}{-12}\]=  \[\frac{1}{4}\]. Let's consider P, Q and R are non- collinear points, draw lines joining these points. The three points A (2, 4), B (4, 6) and C (6, 8)are lying on the same straight line L. These three points are said to be collinear points. ‘prefix 'co' and the word 'linear.' If a point R lies on the line, then points P , Q &  R lie on the same line and are said to be collinear points.