Prove-that-the-length-of-perpendicular-drawn-from-the-point-z-0-to-the-straight-line-z-z-c-0-is-p-z-0-z-0-c-2-

Tinku Tara June 4, 2023 Algebra 0 Comments

Question Number 19508 by Tinkutara last updated on 12/Aug/17

Prove that the length of perpendicular drawn from the point z_0 to the straight line α^� z + αz^� + c = 0 is p = ∣((α^� z_0 + αz_0 ^� + c)/(2 ∣α∣))∣.

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{perpendicular} \\ $$$$\mathrm{drawn}\:\mathrm{from}\:\mathrm{the}\:\mathrm{point}\:{z}_{\mathrm{0}} \:\mathrm{to}\:\mathrm{the}\:\mathrm{straight} \\ $$$$\mathrm{line}\:\bar {\alpha}{z}\:+\:\alpha\bar {{z}}\:+\:{c}\:=\:\mathrm{0}\:\mathrm{is} \\ $$$${p}\:=\:\mid\frac{\bar {\alpha}{z}_{\mathrm{0}} \:+\:\alpha\bar {{z}}_{\mathrm{0}} \:+\:{c}}{\mathrm{2}\:\mid\alpha\mid}\mid. \\ $$

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Prove-that-the-length-of-perpendicular-drawn-from-the-point-z-0-to-the-straight-line-z-z-c-0-is-p-z-0-z-0-c-2-

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