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Algebra of Perspective

Inspired by an article in Mathematics Teacher by Davis, Zielke and Lickeri, Rational Functions: a New Perspective, March 2011. ( And a lifelong interest in perspective drawing and projective geometry. There are so many interesting algebraic and geometric questions in this situation. In addition to the function question posed in the sketch, could you find a function for apparent length (in the image) based on distance from observer?
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