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Home > News & Articles > What are Collinear Points: Definitions, Examples, Formula, and Applications
Updated on 25th May, 2023 , 4 min read
Three or more points on the same line are referred to as collinear points. The term "collinear" is a composite word comprised of the words "co," which refers to togetherness, and "linear," which denotes a line. On separate planes, collinear points may occur, but not on different lines. It is referred to as collinearity since the points are parallel. Points that do not lie on a straight line are referred to as non-collinear points.
The phrase "collinear is the combination word of two Latin terms, 'col' and 'linear'. 'Col' stands for together, while "linear" is for the line. As a result, collinear points are points that are connected by a single line. For Example:Many real-life examples of collinearity may be found, such as a group of students standing in a straight line, a row of apples stored close to each other, and so on.
More astonishingly, the term collinear has been employed for straightened items, which signifies something is "in a row" or "in a line."
There are several ways to tell if three points are parallel or not. The slope formula, the area of the triangle formula, and the distance formula are the three most often used formulae to determine whether two points are collinear or not. The following is the formula for collinear points-
This approach makes use of the fact that three collinear points can never form a triangle. This indicates that no triangle can be formed if any three points are collinear. As a result, we validate the triangle's points by including them in the calculation for the triangle's area. These points will be regarded as collinear if the area is equal to 0. In other words, the triangle created by three collinear points will only be a line connecting the three points and will not have any area. The formula for a triangle's area, which is used to determine if two points are collinear. Triangle with the specified points (vertices) A(xâ‚, yâ‚), B(xâ‚‚, yâ‚‚), and C(x₃, y₃) is-
We calculate the distance between the first and second points using the distance formula before calculating the distance between the second and third points. After that, we determine if the distance between the first and third points is equal to the total of these two distances. Only if the three points are collinear will this be achievable. We employ the distance formula to determine the separation between two places whose coordinates are known to us. The separation between two points A(xâ‚, yâ‚) and B(xâ‚‚, yâ‚‚) is-
Therefore, if there are three collinear points in positions A, B, and C, then AB + BC = CA will cause these points to be collinear.
To get the slope of the lines that the three points under investigation create, we use the slope formula. The three points are collinear if the three slopes are equal. Three points X, Y, and Z, for instance, will only be collinear if the slope of line XY equals the slope of line YZ equals the slope of line XZ. We employ the slope formula to get the slope of the line connecting two locations.
A line connecting two points gradient P (xâ‚, yâ‚) and Q (xâ‚‚, yâ‚‚) is-
There are two ways to determine if the three points are parallel, and they are as follows-
Applications of collinear points in daily life include keeping a set of balls in a straight line or having pupils stand in a straight line during an assembly. Collinear points play a crucial role in resolving practical Euclidean geometry issues.
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By - Nikita Parmar 2023-08-25 09:48:44 , 11 min readAns. A group of three or more points that are located along the same straight line are called collinear points. On separate planes, collinear points may occur, but not on different lines.
Ans. Non-collinear points are those that do not all lie on the same line at a given location.
Ans. Collinear points are referenced together, although their names are written in the standard fashion that is used to mark any point using capital letters. Accordingly, we may say that points A, B, and C are collinear if they form a straight line.
Ans. Collinear points are those that have two or more points that are on the same line.
Ans. Yes, a straight line can be drawn through collinear points.
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