Math Example--Coordinate Geometry--Distance Formula: Example 10

Topic

Geometry

Description

This example illustrates the use of the distance formula to calculate the distance between two points on a coordinate plane. The points (1, 6) and (10, -3) are plotted on a graph, and the distance between them is determined using the formula: √((1 - 10)² + (6 - (-3))²) = √(9^2 + 9^2) = √162 = 9√2.

The distance formula is a key concept in coordinate geometry, allowing students to find the length of a line segment given the coordinates of its endpoints. This collection of examples showcases various applications of the formula, helping students understand its versatility in solving geometric problems across different scenarios, including points in different quadrants and resulting in irrational distances.

Providing multiple worked-out examples is essential for students to fully comprehend the distance formula and its applications. By observing the formula in action across different contexts, students can develop a more robust understanding of how to apply it effectively. This approach also reinforces the step-by-step process of using the formula, enabling students to tackle similar problems with confidence.

Teacher Script: "In this tenth example, we're working with the points (1, 6) and (10, -3). Notice how these points are quite far apart and in different quadrants. As we apply the distance formula, pay attention to how this affects our calculation. What do you notice about our final answer? Why do we leave it in the form 9√2 instead of calculating a decimal approximation?"

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