collinear points
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. These points can be anywhere on the line, and they do not need to be adjacent to each other.
To determine if three points are collinear, one method is to calculate the slope between each pair of points. If the slopes between all pairs are equal, then the points are collinear.
Let’s say we have three points: A(x₁, y₁), B(x₂, y₂), and C(x₃, y₃).
To check for collinearity, we can use the slope formula:
Slope of AB = (y₂ – y₁) / (x₂ – x₁)
Slope of BC = (y₃ – y₂) / (x₃ – x₂)
Slope of AC = (y₃ – y₁) / (x₃ – x₁)
If the three slopes are equal, then the points A, B, and C are collinear.
For example, let’s consider three points: A(2, 3), B(4, 6), and C(6, 9). We can calculate the slopes:
Slope of AB = (6 – 3) / (4 – 2) = 3 / 2
Slope of BC = (9 – 6) / (6 – 4) = 3 / 2
Slope of AC = (9 – 3) / (6 – 2) = 6 / 4 = 3 / 2
Since the three slopes are equal (all are 3/2), we can conclude that the points A, B, and C are collinear.
Remember that collinear points can exist in any coordinate system, including 2D and 3D. Additionally, more than three points can be collinear as long as they lie on the same line.
More Answers:
Understanding Congruent Angles and Their Complements in GeometryUnderstanding the Corresponding Angles Theorem: Exploring the Congruency of Corresponding Angles when Parallel Lines are Cut by a Transversal
Understanding Alternate Exterior Angles: Properties and Proof of Congruence in Parallel Lines