Math Example--Coordinate Geometry--Distance Formula: Example 16

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, -2) and (9, -10) are plotted on a graph, and the distance between them is determined using the formula: √((-1 - 9)² + (-2 - (-10))²) = √((-10)² + 8²) = 2√41.

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 with negative coordinates and resulting in simplified radical expressions.

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 sixteenth example, we're working with the points (-1, -2) and (9, -10). Notice how these points are quite far apart on the coordinate plane. As we apply the distance formula, pay attention to how we simplify our final answer. Why do we leave our answer in the form of 2√41 instead of calculating a decimal approximation? How might this exact form be useful in further calculations?"

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