Question Number 138417 by bemath last updated on 13/Apr/21
$$ \\ $$the x axis is transformed with respect to the line y = 2x +2, determine the equation for the image
Answered by EDWIN88 last updated on 14/Apr/21
$${let}\:{y}={mx}+{n}\:{be}\:{the}\:{image}\:{of}\:{x}−{axis} \\ $$$${where}\:{slope}=\:{m}\:=\:\mathrm{tan}\:\mathrm{2}\alpha\:;\:\left[\:\mathrm{tan}\:\alpha=\mathrm{2}\:\right] \\ $$$${m}\:=\:\frac{\mathrm{2}.\mathrm{2}}{\mathrm{1}−\mathrm{4}}\:=\:−\frac{\mathrm{4}}{\mathrm{3}}.\:{The}\:{line}\:{y}={mx}+{n}\: \\ $$$${passes}\:{through}\:{at}\:{point}\:\left(−\mathrm{1},\mathrm{0}\right)\:.\: \\ $$$${so}\:{we}\:{get}\:{y}=−\frac{\mathrm{4}}{\mathrm{3}}\left({x}+\mathrm{1}\right)+\mathrm{0} \\ $$$$\Leftrightarrow\:{y}\:=\:−\frac{\mathrm{4}}{\mathrm{3}}{x}−\frac{\mathrm{4}}{\mathrm{3}}.\: \\ $$
Commented by EDWIN88 last updated on 14/Apr/21