Point-To-Line Distance Formula: Geometric Proof #2


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    Published on Jan 04, 2021
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    In this video I go over yet another video on deriving the distance formula between a line and a point. This time I solve it using a second Geometric Proof which is very similar to the first method but this time I use an ingenious strategy of identifying two triangles with identical areas but one of which contains the distance from the point to the line. To do this I move the triangle formed by the slope of the line directly on top of the other triangle which contains the distance. Thus we can develop two formulas for the overall area by identifying two different amplitudes or heights, and bases of the triangles. And as in my other derivations, the proof is only valid for slanted lines but nonetheless the final result is applicable for horizontal and vertical lines. This is a great video to understand the many different methods, as well as some ingenious thinking outside the box methods, that can be used to solve the same exact problem, so make sure to watch this video!

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    Related Videos:

    Point-To-Line Distance Formula: Alternative Formula: https://youtu.be/z56Gx6m9uqs
    Point-To-Line Distance Formula: Geometric Proof #1: https://youtu.be/9ilcXZn9CfE
    Point-To-Line Distance Formula: Algebraic Proof: https://youtu.be/tngPrM2d-OM
    Simple Proof of the Pythagorean Theorem: http://youtu.be/yt-EJlbJQp8
    Negative Reciprocals and Perpendicular Lines: http://youtu.be/Ue7FmrfmuX4 .

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