Calculating the Shortest Distance Between a Point and a Line

Miacademy & MiaPrep Learning Channel

In this math lesson, Justin guides students through the geometric and algebraic process of finding the shortest distance between a specific point and a line on a coordinate plane. The video begins by introducing the concept of "desire paths"—natural paths worn into the ground by people taking the most efficient route—to intuitively explain why the shortest path is a straight line. It then transitions to the mathematical proof, demonstrating that on a graph, this shortest path is always the segment perpendicular to the given line. The content covers several critical high school math concepts, including calculating slope (rise over run), understanding the "opposite reciprocal" relationship between perpendicular slopes, finding intersection points on a grid, and applying the distance formula. Through visual demonstrations and step-by-step practice problems, students learn to combine algebraic equations with geometric reasoning to solve complex problems. This video is highly valuable for Geometry and Algebra II classrooms as it bridges the gap between visual intuition and algebraic rigor. It provides a clear, methodical approach to a multi-step procedure that often confuses students. Teachers can use this resource to introduce the topic of distance in the coordinate plane, reinforce the concept of perpendicular slopes, or as a review tool for simplifying radicals and using the distance formula in context.