Math Example--Coordinate Geometry--Distance Formula: Example 17

Topic

Geometry

Description

This example demonstrates the application of the distance formula to find the horizontal distance between two points on a coordinate plane. The points (-2, -7) and (3, -7) are plotted on a graph, and the distance between them is calculated using the formula: √((-2 - 3)² + (-7 + 7)²) = √((-5)² + 0) = 5.

The distance formula is a fundamental tool in coordinate geometry, derived from the Pythagorean theorem. It enables students to calculate the length of a line segment given the coordinates of its endpoints. This collection of examples illustrates various scenarios where the distance formula can be applied, helping students understand its versatility and importance in solving geometric problems, including cases with horizontal distances and negative coordinates.

Presenting multiple worked-out examples is crucial for students to fully grasp the concept of the distance formula. By seeing the formula applied in different contexts, such as points with the same y-coordinate, students can develop a deeper understanding of how to use it effectively. This approach also helps reinforce the steps involved in applying the formula, making it easier for students to solve similar problems independently.

Teacher Script: "Let's examine our seventeenth example of using the distance formula. We have two points on our coordinate plane: (-2, -7) and (3, -7). Notice that these points have the same y-coordinate, creating a horizontal line. As we work through this example, think about how this affects our calculation. What happens to the second term under the square root? How does this simplify our calculation, and why is our final answer a whole number?"

For a complete collection of math examples related to Geometry click on this link: Math Examples: Distance Formula Collection.