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One Response
Project P onto the direction v = B−A: t = ((P−A)·v)/(v·v) and foot H = A + t v; here v=(4,1), (P−A)=(1,5), so t=9/17 and H=(53/17, 43/17). Think of it as P’s shadow dropped onto AB by a light shining perpendicular to the line; see vector projections at https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces/dot-cross-products/a/linear-algebra-vector-projections.