distance formula worksheet pdf

Guri Bee

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22-10-2024

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Mastering the Distance Formula: A Comprehensive Worksheet Guide

The distance formula is a fundamental concept in geometry, allowing us to calculate the distance between two points in a coordinate plane. Understanding and applying this formula is crucial for various mathematical problems, from finding the length of line segments to determining the perimeter of geometric shapes.

This article will explore the distance formula through the lens of a helpful worksheet, providing you with a step-by-step guide and insightful explanations.

Understanding the Distance Formula

The distance formula is derived from the Pythagorean theorem and states:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

• d represents the distance between the two points
• (x₁, y₁) are the coordinates of the first point
• (x₂, y₂) are the coordinates of the second point

Worksheet Walkthrough: A Step-by-Step Guide

Let's delve into a sample worksheet and break down the process of solving distance formula problems:

Example 1:

• Problem: Find the distance between the points (2, 3) and (5, 7).

• Solution:

1. Identify the coordinates:

   • (x₁, y₁) = (2, 3)
   • (x₂, y₂) = (5, 7)

2. Substitute the values into the formula:

   • d = √[(5 - 2)² + (7 - 3)²]

3. Simplify the equation:

   • d = √[(3)² + (4)²]
   • d = √(9 + 16)
   • d = √25

4. Calculate the final answer:

   • d = 5

Therefore, the distance between the points (2, 3) and (5, 7) is 5 units.

Example 2:

• Problem: A triangle has vertices at points A (1, 2), B (4, 5), and C (7, 2). Calculate the perimeter of the triangle.

• Solution:

1. Find the distance between each pair of vertices:

   • AB: d = √[(4 - 1)² + (5 - 2)²] = √(9 + 9) = √18 = 3√2
   • BC: d = √[(7 - 4)² + (2 - 5)²] = √(9 + 9) = √18 = 3√2
   • AC: d = √[(7 - 1)² + (2 - 2)²] = √(36 + 0) = √36 = 6

2. Add the distances to find the perimeter:

   • Perimeter = AB + BC + AC = 3√2 + 3√2 + 6 = 6√2 + 6

Therefore, the perimeter of the triangle is 6√2 + 6 units.

Key Takeaways:

• Practice makes perfect: The distance formula may seem daunting at first, but with consistent practice, it becomes a breeze. The worksheet provides a structured approach to solving various problems.
• Real-world applications: The distance formula is not limited to abstract mathematical problems. It finds application in areas such as navigation, surveying, and even computer graphics.
• Beyond the formula: Understanding the underlying principles of the Pythagorean theorem and coordinate geometry is essential for mastering the distance formula.

Additional Resources:

• Khan Academy - Distance Formula
• Purplemath - Distance Formula

By diligently working through a distance formula worksheet, you'll gain a solid understanding of this fundamental concept and enhance your problem-solving skills in various mathematical contexts. Remember, practice is key!