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  • The line is rotated through an angle <img alt="\mathrm{\frac{\pi}{

The line \mathrm{3 x-4 y+7=0} is rotated through an angle \mathrm{\frac{\pi}{4}} in clockwise direction about the point (-1,1).The equation of the line in its new position is

Option: 1

\mathrm{7 y+x-6=0}


Option: 2

\mathrm{7 y-x-6=0}


Option: 3

\mathrm{7 y+x+6=0}


Option: 4

\mathrm{7 y-x+6=0}


Answers (1)

best_answer

As (-1,1) is a point on \mathrm{3 x-4 y+7=0}, the rotation is possible.
Slope of the given line \mathrm{=\frac{3}{4}} Slope of the line in its new position
\mathrm{=\frac{\frac{3}{4}-1}{1+\frac{3}{4}}=-\frac{1}{7}}
The required equation is \mathrm{y-1=-\frac{1}{7}(\mathrm{x}+1)\, }
\mathrm{or, \, 7 y+x-6=0 }.

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