How to Calculate the Distance Between a Point and a Line

The Organic Chemistry Tutor

This video provides a step-by-step tutorial on calculating the perpendicular distance between a point and a linear graph in both two-dimensional and three-dimensional space. The narrator walks through three specific examples: a standard 2D line equation, a 2D line equation involving fractions that requires conversion to standard form, and a 3D equation (representing a plane) involving x, y, and z coordinates. The tutorial emphasizes using the specific distance formula involving absolute values and square roots. The key themes explored include understanding the standard form of linear equations ($Ax + By + C = 0$), identifying coefficients, and substituting values into the distance formula. The video demonstrates algebraic manipulation skills, such as clearing fractions from an equation to simplify the coefficients before calculation. It also bridges the gap between 2D geometry and 3D coordinate geometry by showing how the distance formula extends naturally by adding a $z$-term. For educators, this video is an excellent resource for Algebra II, Pre-Calculus, or Geometry classrooms. It can be used to introduce the concept of distance beyond simple point-to-point calculations, reinforcing the geometric interpretation of algebraic equations. The clear, worked-out examples serve as models for students to follow, helping them master the procedural aspects of these calculations while visualizing the concept of perpendicular distance.