How to show that three points are collinear in coordinate geometry?
Answers
How to show that three points are collinear in coordinate geometry:
Method 1. Finding the area
When the coordinates of the points points are given (x₁, y₁), (x₂, y₂) and (x₃, y₃), we find the value of the following determinant being 0.
| x₁ y₁ 1 |
| x₂ y₂ 1 |
| x₃ y₃ 1 |
Note - This determinant gives half the value of area of a triangle in coordinate geometry.
Method 2. Satisfying the line passing through the points
In this method, find the equation of the straight line passing through the two points (x₁, y₁) and (x₂, y₂) using point-point form or slope-value form. See the following,
y - y₁= (y₂ - y₁)/(x₂ - x₁) * (x - x₁)
Now rearrange the terms in the left side and write an equation f(x, y) = 0. Satisfy f(x, y) by the third point (x₃, y₃). If the point satisfies f(x, y), i.e., f(x₃, y₃) = 0, then the three points are colinear.
See some problems related to collinear property here:
1. Show that the points (1, 1), (2, 2) and (3, 3) are collinear.
- brainly.in/question/8259036
2. Show that the points (2, 3), (8, 11) and (-1, -1) are collinear.
- brainly.in/question/8230024