## Collinear points Chapter 1 (p. 4)

### In mathematics, collinear points refer to a set of points that lie on the same straight line

In mathematics, collinear points refer to a set of points that lie on the same straight line. More specifically, any two points can form a line, but if there are three or more points that lie on the same line, they are termed as collinear points.

Let’s consider an example to understand this concept better. Suppose we have three points A, B, and C. To determine if they are collinear, we need to check if they lie on the same line.

One method to check collinearity is to find the slopes of the line segments formed by the points. If the slopes of any two line segments are equal, then the points are collinear.

To calculate the slope of a line segment, we use the formula:

slope = (change in y-coordinates) / (change in x-coordinates)

For instance, let’s say A has coordinates (2, 4), B has coordinates (6, 9), and C has coordinates (8, 14). We can calculate the slopes of line segments AB and BC to determine if the points are collinear.

Step 1: Calculate the slope of AB.

change in y-coordinates = 9 – 4 = 5

change in x-coordinates = 6 – 2 = 4

slope of AB = (5) / (4) = 5/4

Step 2: Calculate the slope of BC.

change in y-coordinates = 14 – 9 = 5

change in x-coordinates = 8 – 6 = 2

slope of BC = (5) / (2) = 5/2

Since the slope of AB is not equal to the slope of BC, we can conclude that points A, B, and C are not collinear.

However, it is important to note that this is just one method to determine collinearity. Another method is to use the concept of area. If the area of the triangle formed by the points is zero, then the points are collinear.

In conclusion, collinear points refer to points that lie on the same straight line. They can be determined by calculating the slopes of the line segments formed by the points or by checking if the area of the triangle formed by the points is zero.

## More Answers:

Exploring Adjacent Angles: Definition, Types, and RelationshipsDiscover the Properties and Applications of Angle Bisectors in Mathematics

Master the Fundamental Concepts of Mathematics: Sets, Logic, Number Systems, Relations, and Functions – Chapter 1 of Axiom