Foot of perpendicular to a given Line Calculator

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

• 1. Introduction to the Foot of perpendicular from a point to a line
• 2. What is the Formulae used ?
• 3. How do I calculate the Foot perpendicular from a point to a line?
• 4. Why choose our the Foot of perpendicular from a point to a line 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 Foot of perpendicular from a point to a line

Welcome to the realm of geometry, where we'll unravel the concept of finding the foot of the perpendicular from a point to a line. This geometric operation is crucial in understanding distances and relationships between points and lines. In this guide, we'll explore the definition, formula, and practical applications of finding the foot of the perpendicular, equipping you with the tools to tackle geometric problems effectively.
$\bold{Definition}$
The foot of the perpendicular from a point to a line is the point on the line that forms a right angle (90 degrees) with the given point. It represents the shortest distance between the end and the line, creating a perpendicular line segment.

2. What is the Formulae used?

To find the foot of the perpendicular from a point (h, k) from a point (p, q) to a line ax + by + c = 0
we use the formula derived from the concept of perpendicular distance from a point to a line:
$\frac{h - p}{a} = \frac{k - q}{b} = \frac{-(ap + bq + c)}{(a^2 + b^2)}$

3. How do I calculate the Foot of the perpendicular from a point to a line?

Identify the point and equation of the line in general standard form.
Plug these values into the formula and obtain the coordinates of the foot of perpendicular.

4. Why choose our Foot of the perpendicular from a point to a line 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 Foot of the perpendicular from a point to a line.

6. How to use this calculator

This calculator will help you find the foot of the perpendicular from a point to a line.
In the given input boxes, you have to put the value of the coordinates of the point and the equation of a line.
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

$\bold{Question:1}$
Find the coordinates of the foot of the perpendicular from the point P (2, 3) about the line 3x - 4y + 5 = 0.
$\bold{Solution:1}$
Using the above-given formula:
$\frac{h - 2}{3} = \frac{k - 3}{-4} = \frac{((3)(2) + (-4)(3) + 5)}{((3)^2 + (-4)^2)}$
solving for (h, k) = ($\frac{11}{7}, \frac{25}{7}$)

8. Frequently Asked Questions (FAQs)

What is the foot of the perpendicular in geometry?

The foot of the perpendicular is the point on a line that forms a right angle with a given moment, representing the shortest distance between the end and the line.

How is the foot of the perpendicular calculated?

The foot of the perpendicular is calculated using the formula derived from the concept of perpendicular distance from a point to a line.

Can the foot of the perpendicular be outside the line segment?

No, the foot of the perpendicular always lies on the line segment between the given point and the line.

What happens if the point lies on the line?

If the point lies on the line, the foot of the perpendicular coincides with the given point.

What are some real-life applications of the foot of perpendicular?

The concept of the foot of perpendicular is used in architecture, engineering, and navigation for measuring distances, designing structures, and plotting trajectories.

9. What are the real-life applications?

The foot of the perpendicular finds applications in various fields, including architecture, which is used to design structures with precise dimensions, and surveying, which helps accurately measure distances.

10. Conclusion

Understanding the concept of the foot of the perpendicular and its calculation method is essential in geometry. It provides valuable insights into the relationship between points and lines, enabling accurate measurements and geometric constructions. By mastering the formula and properties of the foot of the perpendicular, you gain the ability to solve geometric problems effectively and apply these concepts in real-life scenarios with confidence. Armed with the knowledge provided in this guide, you're now equipped to explore and utilize the foot of perpendicular in various mathematical and practical contexts.

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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