If A Person Walks From (1, 5) To (7, 2) In A Straight Line, What Is The Shortest Distance They Traveled?

Mar 11, 2025 by ADMIN 105 views

**If a Person Walks from (1, 5) to (7, 2) in a Straight Line, What is the Shortest Distance They Traveled?** ===========================================================

Introduction

In mathematics, particularly in geometry, the shortest distance between two points is a fundamental concept. It is a crucial aspect of understanding various mathematical concepts, including distance, displacement, and trajectory. In this article, we will explore the concept of the shortest distance between two points in a straight line, using a real-world example.

What is the Shortest Distance?

The shortest distance between two points in a straight line is a straight line itself. This is a fundamental property of geometry, and it can be proven using various mathematical techniques. In the context of our example, the shortest distance between the points (1, 5) and (7, 2) is a straight line that connects these two points.

Calculating the Shortest Distance

To calculate the shortest distance between two points in a straight line, we can use the distance formula. The distance formula is a mathematical formula that calculates the distance between two points in a coordinate plane. The formula is as follows:

d = √((x2 - x1)² + (y2 - y1)²)

where d is the distance between the two points, and (x1, y1) and (x2, y2) are the coordinates of the two points.

Applying the Distance Formula

In our example, the coordinates of the two points are (1, 5) and (7, 2). We can plug these values into the distance formula to calculate the shortest distance between the two points.

d = √((7 - 1)² + (2 - 5)²) d = √((6)² + (-3)²) d = √(36 + 9) d = √45

Simplifying the Result

The result of the calculation is √45. However, we can simplify this result by expressing it as a decimal value.

√45 ≈ 6.708

Conclusion

In conclusion, the shortest distance between the points (1, 5) and (7, 2) in a straight line is approximately 6.708 units. This result is obtained by applying the distance formula to the coordinates of the two points.

Frequently Asked Questions

Q: What is the shortest distance between two points in a straight line?

A: The shortest distance between two points in a straight line is a straight line itself.

Q: How do I calculate the shortest distance between two points in a straight line?

A: You can use the distance formula to calculate the shortest distance between two points in a straight line. The distance formula is as follows:

d = √((x2 - x1)² + (y2 - y1)²)

Q: What is the distance formula?

A: The distance formula is a mathematical formula that calculates the distance between two points in a coordinate plane.

Q: How do I apply the distance formula?

A: To apply the distance formula, you need to plug the coordinates of the two points into the formula and calculate the result.

Q: Can I simplify the result of the distance formula?

A: Yes, you can simplify the result of the distance formula by expressing it as a decimal value.

Q: What is the significance of the shortest distance between two points in a straight line?

A: The shortest distance between two points in a straight line is a fundamental concept in mathematics, particularly in geometry. It is used to calculate distances, displacements, and trajectories in various mathematical and real-world applications.

Q: Can I use the shortest distance between two points in a straight line in real-world applications?

A: Yes, the shortest distance between two points in a straight line is used in various real-world applications, including navigation, transportation, and engineering.

Q: How do I use the shortest distance between two points in a straight line in real-world applications?

A: You can use the shortest distance between two points in a straight line to calculate distances, displacements, and trajectories in various real-world applications. For example, you can use it to calculate the distance between two cities, the displacement of an object, or the trajectory of a projectile.

Q: What are some examples of real-world applications of the shortest distance between two points in a straight line?

A: Some examples of real-world applications of the shortest distance between two points in a straight line include:

Navigation: Calculating the shortest distance between two points to determine the most efficient route.
Transportation: Calculating the shortest distance between two points to determine the most efficient route for transportation.
Engineering: Calculating the shortest distance between two points to determine the most efficient trajectory for a projectile or a moving object.

Q: Can I use the shortest distance between two points in a straight line in other mathematical concepts?

A: Yes, the shortest distance between two points in a straight line is used in various mathematical concepts, including:

Geometry: Calculating distances, displacements, and trajectories in various geometric shapes.
Trigonometry: Calculating distances, displacements, and trajectories using trigonometric functions.
Calculus: Calculating distances, displacements, and trajectories using differential equations and integral calculus.

Q: How do I use the shortest distance between two points in a straight line in other mathematical concepts?

A: You can use the shortest distance between two points in a straight line to calculate distances, displacements, and trajectories in various mathematical concepts. For example, you can use it to calculate the distance between two points in a geometric shape, the displacement of an object in a trigonometric function, or the trajectory of a projectile in a differential equation.

Q: What are some examples of mathematical concepts that use the shortest distance between two points in a straight line?

A: Some examples of mathematical concepts that use the shortest distance between two points in a straight line include:

Geometry: Calculating distances, displacements, and trajectories in various geometric shapes, such as triangles, circles, and polygons.
Trigonometry: Calculating distances, displacements, and trajectories using trigonometric functions, such as sine, cosine, and tangent.
Calculus: Calculating distances, displacements, and trajectories using differential equations and integral calculus.

Q: Can I use the shortest distance between two points in a straight line in other fields?

A: Yes, the shortest distance between two points in a straight line is used in various fields, including:

Physics: Calculating distances, displacements, and trajectories in various physical systems, such as mechanics, electromagnetism, and thermodynamics.
Computer Science: Calculating distances, displacements, and trajectories in various computer science applications, such as graphics, game development, and artificial intelligence.
Engineering: Calculating distances, displacements, and trajectories in various engineering applications, such as mechanical engineering, civil engineering, and aerospace engineering.

Q: How do I use the shortest distance between two points in a straight line in other fields?

A: You can use the shortest distance between two points in a straight line to calculate distances, displacements, and trajectories in various fields. For example, you can use it to calculate the distance between two objects in a physical system, the displacement of an object in a computer graphics application, or the trajectory of a projectile in an engineering application.

Q: What are some examples of fields that use the shortest distance between two points in a straight line?

A: Some examples of fields that use the shortest distance between two points in a straight line include:

Physics: Calculating distances, displacements, and trajectories in various physical systems, such as mechanics, electromagnetism, and thermodynamics.
Computer Science: Calculating distances, displacements, and trajectories in various computer science applications, such as graphics, game development, and artificial intelligence.
Engineering: Calculating distances, displacements, and trajectories in various engineering applications, such as mechanical engineering, civil engineering, and aerospace engineering.