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- By using the sets of three collinear points, we can draw only one straight line. A straight line can always be drawn by using two points. So, here we can say that two points are always collinear points. Uncertainty comes when it is more than two points; hence we check three points of collinearity.
www.geeksforgeeks.org/collinear-points/Collinear Points: Definition, Formula & How to Find Collinearity
Suppose the points A (x 1, y 1), B (x 2, y 2) and C (x 3, y 3) are collinear, then the Conditions for Collinearity of Three Points are: (i) Slope of AB = Slope of BC. (ii) AB + BC = AC (or) AB + AC = BC (or) AC + BC = AB. This can be proved using the distance formula in coordinate geometry.
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Aug 13, 2024 · In this article, we will discuss the concept of collinear points, collinear point definition, collinear point meaning, and properties. We will also know how to determine the three points collinearity by different methods.
- Distance Formula. One of the ways to prove that three points are collinear is by using the distance formula. The distance formula can calculate the distance between two points in a Cartesian plane.
- Slope Formula. Another method to prove collinearity of three points is by using the slope formula. The slope formula provides a way to calculate the slope of a line that connects two points in a Cartesian plane.
- Vector Algebra. A third method to prove collinearity of three points is by using vector algebra. Vector algebra can be used to determine whether three points are collinear or not by finding the cross product of two vectors that connect the three points.
- Using the Intersection of Lines. You can also use the intersection of lines to prove collinearity of three points. By drawing lines through pairs of points, you can find the intersection point of these lines.
- Slope Formula
- Area of Triangle Formula
- Distance Formula
We apply the slope formula to find the slope of lines formed by the 3 points under consideration. If the 3 slopes are equal, then the three points are collinear. For example, if we have three points X, Y, and Z, the points will be collinear only if the slope of line XY = slope of line YZ = slope of line XZ. To calculate the slope of the line joinin...
In this method, we use the fact that a triangle cannot be formed by three collinear points. This means if any 3 points are collinear they cannot form a triangle. Therefore, we check the points of the triangle by using them in the formula for the area of a triangle. If the areais equal to 0, then those points will be considered to be collinear. In o...
Using the distance formula, we find the distance between the first and the second point, and then the distance between the second and the third point. After this, we check if the sum of these two distances is equal to the distance between the first and the third point. This will only be possible if the three points are collinear points. To calculat...
We will find the condition of collinearity of three given points by using the concept of slope. Let P (x1 1, y1 1) , Q (x2 2, y2 2) and R (x3 3, y3 3) are three given points. If the points P, Q and R are collinearity then we must have, Slop of the line PQ = slop of the line PR.
In general, three points A, B and C are collinear if the sum of the lengths of any two line segments among AB, BC and CA is equal to the length of the remaining line segment, that is, either AB + BC = AC or AC + CB = AB or BA + AC = BC.
People also ask
Why do we check three points of collinearity?
Can three points be collinear?
How to calculate collinearity of 3 points?
What is the condition for collinearity of 3 points?
Which method is used to determine if all three points are collinear?
What if 3 points are collinear if ab + bc = ca?
The different methods to check the Collinearity of 3 points are the Distance Formula, Slope Formula, the Area of a Triangle Formula, and Equation Method. The set of points is said to be collinear in the vector form if there exists a linear relation between them, such that the sum of the coefficients in it is zero.
