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\\n
Answered by EDWIN88 last updated on 14/Apr/21
![let y=mx+n be the image of x−axis where slope= m = tan 2α ; [ tan α=2 ] m = ((2.2)/(1−4)) = −(4/3). The line y=mx+n passes through at point (−1,0) . so we get y=−(4/3)(x+1)+0 ⇔ y = −(4/3)x−(4/3).](Q138478.png)
$${let}\:{y}={mx}+{n}\:{be}\:{the}\:{image}\:{of}\:{x}−{axis} \\ $$ $${where}\:{slope}=\:{m}\:=\:\mathrm{tan}\:\mathrm{2}\alpha\:;\:\left[\:\mathrm{tan}\:\alpha=\mathrm{2}\:\right] \\ $$ $${m}\:=\:\frac{\mathrm{2}.\mathrm{2}}{\mathrm{1}−\mathrm{4}}\:=\:−\frac{\mathrm{4}}{\mathrm{3}}.\:{The}\:{line}\:{y}={mx}+{n}\: \\ $$ $${passes}\:{through}\:{at}\:{point}\:\left(−\mathrm{1},\mathrm{0}\right)\:.\: \\ $$ $${so}\:{we}\:{get}\:{y}=−\frac{\mathrm{4}}{\mathrm{3}}\left({x}+\mathrm{1}\right)+\mathrm{0} \\ $$ $$\Leftrightarrow\:{y}\:=\:−\frac{\mathrm{4}}{\mathrm{3}}{x}−\frac{\mathrm{4}}{\mathrm{3}}.\: \\ $$
Commented byEDWIN88 last updated on 14/Apr/21
