Math Example--Coordinate Geometry--Distance Formula: Example 13

Topic

Geometry

Description

This example demonstrates the application of the distance formula to find the distance between two points on a coordinate plane. The points (-10, 6) and (-1, -1) are plotted on a graph, and the distance between them is calculated using the formula: √((-10 - (-1))² + (6 - (-1))²) = √((-9)² + 7²) = √130.

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 points in different quadrants and resulting in irrational distances.

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 both positive and negative coordinates, 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 thirteenth example of using the distance formula. We have two points on our coordinate plane: (-10, 6) and (-1, -1). Notice that these points are in different quadrants. As we work through this example, think about how this affects our calculation. Why do we end up with an irrational number as our final answer? How does this relate to the Pythagorean theorem?"

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