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Geometry of distance of a point from a line

The conic sections are a set of topics I'm not particularly well-versed in, and I'd like some advice so that I can build a bit of intuition. Geometric approaches usually don't bother me too much, but the formulas for computing distance from a point (x_{1},y_{1}) to a line Ax + By + C = 0 or y = mx + b definitely aren't sinking in, and I suspect it's because I don't fully understand similarity between right triangles.

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Re: Geometry of distance of a point from a line

Triangles ABD and EGF are similar right? Therefore AB/EG = AD/EF.

Re: Geometry of distance of a point from a line

What proves that these two triangles are similar to each other though?