Determining Collinear Points in Geometry: How to Check if Three or More Points Lie on the Same Line+ Improve your geometrical knowledge by understanding the concept of collinear points and learn how to determine if three or more points lie on the same straight line

Collinear Points

In geometry, collinear points refer to three or more points that lie on the same straight line

In geometry, collinear points refer to three or more points that lie on the same straight line. A straight line can be thought of as an infinitely long and infinitely thin path that extends in both directions. If three or more points lie on this path, they are said to be collinear.

To determine if three points are collinear, you need to check if the slope of the line passing through any two of the points is the same. If the slopes are equal, the points are collinear.

For example, let’s consider three points: A(2, 3), B(4, 6), and C(6, 9). To check if these points are collinear, we can calculate the slope of the line passing through points A and B, and then the slope of the line passing through points B and C.

The slope of a line can be found using the formula:
slope = (change in y)/(change in x) = (y2 – y1)/(x2 – x1)

For the line passing through A and B:
slope_AB = (6 – 3)/(4 – 2) = 3/2

For the line passing through B and C:
slope_BC = (9 – 6)/(6 – 4) = 3/2

As both slopes are equal, we can conclude that points A, B, and C are collinear.

It is important to note that if the slopes of any two pairs of points are not equal, then the points are not collinear. Additionally, if only two points are given, they are technically collinear since any two points uniquely determine a line.

More Answers: