Distance Between a Point and a Line Proof - Algebraic Method

Explore a comprehensive 32-minute video tutorial on deriving the distance formula between a point and a line using algebraic methods. Learn the step-by-step process, including converting the line equation to slope-intercept form, finding the perpendicular line, solving a linear system for the intersection point, and applying the distance formula. Follow along as the instructor breaks down complex calculations, simplifies expressions, and arrives at the final formula: d = (|ax_1 + by_1 + c|) / (sqrt(a^2 + b^2)). Gain a deeper understanding of geometric concepts and algebraic techniques through this detailed derivation, suitable for students and enthusiasts seeking to master this fundamental mathematical principle.

Introduction
Sketch of setting up a perpendicular line segment
Placing the line in slope-intercept form
Finding the perpendicular line
Finding x_2
Finding y_2
Setting up the distance formula
Simplifying x_2 - x_1^2
Simplifying y_2 - y_1^2
Final steps