Section formula Calculator

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

• 1. Introduction to the Section Formula
• 2. What is the Formulae used ?
• 3. How do I calculate the internal & external division by Section Formula?
• 4. Why choose our Section Formula 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 Section Formula

Coordinate geometry is a fundamental branch of mathematics that studies geometric figures using algebraic techniques. Among its many concepts, the section formula is a powerful tool for determining the coordinates of a point that divides a line segment into a given ratio. In this comprehensive guide, we'll delve into the intricacies of the section formula, exploring internal and external divisions and their applications.
$\bold{Definition}$
The section formula, also known as the division formula, is a mathematical principle used to find the coordinates of a point that divides a line segment into a given ratio. It provides a systematic approach to determining the position of a point along a line segment in coordinate geometry.

2. What is the Formulae used?

For $\bold{Internal}$ division
If a point P divides the line segment joining points A$(x_1, y_1)$ and B$(x_2, y_2)$ internally in the ratio m : n, then the coordinates of point P are given by:
$\color{black}\bold{(x, y) = (\frac{(m.x_2 + n.x_1)}{m+n}, \frac{(m.y_2 + n.y_1)}{m-n})}$

For $\bold{External}$ division If a point P divides the line segment joining points A$(x_1, y_1)$ and B$(x_2, y_2)$ internally in the ratio m : n, then the coordinates of point P are given by:
$\color{black}\bold{(x, y) = (\frac{(m.x_2 - n.x_1)}{m-n}, \frac{(m.y_2 - n.y_1)}{m-n})}$

3. How do I calculate the internal & external division by Section Formula?

Calculating the division point of a line joining two points involves a series of straightforward steps:
Select the division system type $\bold{Internal}$ or $\bold{External}$
Identify the given point's coordinates and division ratio.
Plug these values into the formula for the section formula.
Calculate the result by reducing fraction.

4. Why choose our Section Formula 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 the concept of how to find the internal & external division by Section Formula.

6. How to use this calculator

This calculator will help you to find the internal & external division by Section Formula.
In the given input boxes, you have to put the value of the coordinates of the points $\bold{(x_1, y_1)}$ & $\bold{(x_2, y_2)}$ and the value of m and n.
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

$\bold{Question:1}$
Let A(2, 3) and B(6, 9) be the endpoints of a line segment. Find the coordinates of a point P that divides AB internally in the ratio 2:3.
$\bold{Solution}$
By using the above given formula for $\color{black}\bold{Division \space point = (x, y) = (\frac{(m.x_2 + n.x_1)}{m+n}, \frac{(m.y_2 + n.y_1)}{m+n})}$
$\color{black}\bold{(x, y) = (\frac{(2.6 + 3.2)}{2+3}, \frac{(2.9 + 3.3)}{2+3})}$
Coordinates of Internal Division point M = (3.6, 6.6)

$\bold{Question:2}$
Let A(1, 2) and B(5, 8) be the endpoints of a line segment. Find the coordinates of a point P that divides AB externally in the ratio 3:2.
$\bold{Solution}$
By using the above given formula for $\color{black}\bold{Division \space point = (x, y) = (\frac{(m.x_2 - n.x_1)}{m-n}, \frac{(m.y_2 - n.y_1)}{m-n})}$
$\color{black}\bold{(x, y) = (\frac{(3.5 + 2.1)}{3-2}, \frac{(3.8 + 2.2)}{3-2})}$
Coordinates of External Division point M = (13, 22)

8. Frequently Asked Questions (FAQs):-

What is the section formula?

The section formula is a mathematical principle used to find the coordinates of a point that divides a line segment into a given ratio.

How do you find the coordinates of a point using the section formula?

To find the coordinates of a point using the section formula, you need the coordinates of the endpoints of the line segment and the ratio in which the segment is divided.

What is the difference between internal and external divisions?

Internal division occurs when the point lies between the endpoints of the segment, while external division occurs when the point lies outside the segment.

Can the section formula be used in three dimensions?

Yes, the section formula can be extended to three dimensions, allowing for determining coordinates in space.

What are some real-life applications of the section formula?

The section formula finds applications in various fields, including architecture, engineering, and computer graphics, where it is used to determine the position of objects relative to reference points.

9. What are the real-life applications?

The section formula is applied in various real-life scenarios, such as determining the location of a point relative to two reference points in surveying, proportionally dividing resources, and designing structures with specific dimensions.

10. Conclusion

The section formula in coordinate geometry is a powerful tool for determining the coordinates of a point that divides a line segment into a given ratio. By understanding the principles of internal and external division and their applications, you gain valuable insights into geometric concepts with wide-ranging practical implications. Armed with the formula, examples, and insights in this guide, you can apply the section formula in various mathematical and real-world scenarios.

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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