Test of collinearity of three points in 2D Calculator

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$\bold{Table \space of \space Content}$

• 1. Introduction to the Testing collinearity of three points
• 2. What is the Formulae used ?
• 3. How do I check the collinearity of three points?
• 4. Why choose our Testing collinearity of three points Calculator?
• 5. A Video for explaining this concept
• 6. How to use this calculator ?
• 7. Solved Examples
• 8. Frequently Asked Questions (FAQs)
• 9. What are the real-life applications?
• 10. Conclusion

1. Introduction to the Testing collinearity of three points

Understanding collinearity – the alignment of points along a straight line – is fundamental in geometry. In this guide, we'll explore how to check the collinearity of three points in 2D space. By grasping the concepts and methods involved, you'll gain insights into the spatial relationships between points, which are essential for various geometric analyses.
$\bold{Definition}$
Collinearity refers to the property of three or more points on the same straight line. In 2D space, determining collinearity involves assessing whether three points are aligned. This concept is crucial in geometry, facilitating geometric constructions, calculations, and problem-solving.

2. What is the Formulae used?

The collinearity of three points $(x_1, y_1), (x_2, y_2)$, and (x_3, y_3) in 2D space can be checked using the determinant method. If the determinant of the matrix formed by these points is zero, they are collinear. The formula is:
$\bold{Area} = \frac{1}{2}|x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$ = 0

3. How do I calculate the Testing collinearity of three points?

Identify the coordinates of the vertices.
Plug these values into the formula and obtain the coordinates of the reflected point.

4. Why choose our Testing collinearity of three points Calculator?

$\bold{Easy \space \space to \space Use}$
Our calculator page provides a user-friendly interface that makes it accessible to both students and professionals. You can quickly input your square matrix and obtain the matrix of minors within a fraction of a second.

$\bold{Time \space Saving \space By \space automation}$
Our calculator saves you valuable time and effort. You no longer need to manually calculate each cofactor, making complex matrix operations more efficient.

$\bold{Accuracy \space and \space Precision}$
Our calculator ensures accurate results by performing calculations based on established mathematical formulas and algorithms. It eliminates the possibility of human error associated with manual calculations.

$\bold{Versatility}$
Our calculator can handle all input values like integers, fractions, or any real number.

$\bold{Complementary \space Resources}$
Alongside this calculator, our website offers additional calculators related to Pre-algebra, Algebra, Precalculus, Calculus, Coordinate geometry, Linear algebra, Chemistry, Physics, and various algebraic operations. These calculators can further enhance your understanding and proficiency.

5. A video based on how to find the Triangle area with vertices.

6. How to use this calculator

This calculator will help you test the collinearity of three points.
In the given input boxes, you have to put the value of the coordinates of the vertices.
After clicking on the Calculate button, a step-by-step solution will be displayed on the screen.
You can access, download, and share the solution.

7. Solved Examples

$\bold{Question}$
Check whether the given points A(1, 2), B(3, 4), and C(5, 1) are collinear or not?
$\bold{Solution}$
Using the above-given formula:
$\bold{Area} = \frac{1}{2}|1(4 - 1) + 3(1 - 2) + 5(2 - 4)|$ = 3 $\ne$ 0
Hence, Given Points are NOT collinear.

8. Frequently Asked Questions (FAQs)

What does it mean for points to be collinear?

Collinear points lie on the same straight line, forming a linear sequence.

How can I check collinearity without using determinants?

You can also check collinearity by calculating the slopes between pairs of points and verifying if they are equal.

What if the determinant is not zero?

If the determinant is nonzero, the points are not collinear and form a triangle or another geometric shape.

Can more than three points be collinear?

Yes, any number of points greater than two can be collinear if they lie on the same line.

Why is collinearity important in geometry?

Collinearity helps in defining and analyzing geometric shapes, constructing figures, and solving problems involving lines and points.

9. What are the real-life applications?

Collinearity finds applications in various real-world scenarios, such as surveying for land development, navigation for route planning, computer graphics for rendering lines and shapes, and architecture for designing structures.

10. Conclusion

Understanding the concept of collinearity and knowing how to check the alignment of points in 2D space is crucial in geometry and beyond. By employing the determinant method or slope calculations, you can determine whether three points are collinear, unlocking insights into their spatial relationships. Explore the examples provided, delve into real-life applications, and embrace the power of geometric analysis in your endeavors. With this knowledge, you can navigate the world of collinearity with confidence and precision, enriching your understanding of geometric principles.

This blog is written by Neetesh Kumar

If you have any suggestions regarding the improvement of the content of this page, please write to me at My Official Email Address: [email protected]

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