let-A-1-1-and-B-0-3-find-image-of-the-line-AB-by-1-translation-t-u-with-u-1-2i-2-rotation-R-w-pi-3-with-w-1-i-

Tinku Tara June 4, 2023 Geometry 0 Comments

Question Number 41521 by maxmathsup by imad last updated on 08/Aug/18

let A(−1,1) and B(0,3) find image of the line (AB) by 1) translation t_u^→ with u^→ (1−2i) 2) rotation R(w,(π/3)) with w(1+i)

$${let}\:{A}\left(−\mathrm{1},\mathrm{1}\right)\:{and}\:{B}\left(\mathrm{0},\mathrm{3}\right)\:\:\:{find}\:\:\:{image}\:{of}\:{the}\:{line}\:\left({AB}\right)\:{by} \\ $$$$\left.\mathrm{1}\right)\:{translation}\:{t}_{\overset{\rightarrow} {{u}}} \:\:\:\:{with}\:\overset{\rightarrow} {{u}}\left(\mathrm{1}−\mathrm{2}{i}\right) \\ $$$$\left.\mathrm{2}\right)\:{rotation}\:{R}\left({w},\frac{\pi}{\mathrm{3}}\right)\:\:{with}\:{w}\left(\mathrm{1}+{i}\right) \\ $$

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