In this video I go over the distance formula between a point and a line once again, but this time take a look at a Geometric Proof. This proof, just line in my earlier Algebraic Proof, is only valid for slanted lines but nonetheless the final result is still applicable for horizontal and vertical lines. The proof uses the fact that we make a triangle between the point and the line, we get an angle that is also shared by a second triangle made by the slope of that line. This connection allows us to determine the distance using just the constants of the Line and coordinates of the point. This is a very unique derivation and is easier to go through than the algebraic proof. This is a great video to understand how there are often many different mathematical approaches that can be used to solve the same problem, so make sure to watch this video!
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Point-to-Line Distance Formula: Geometric Proof #1
Note that just like in the Algebraic Proof, this proof is only valid for slanted lines but the final result nonetheless is applicable to horizontal and vertical lines!
