The line 3 x-4 y+7=0 is rotated through an angle ( (π)/(4) ) in the...

The line

3 x-4 y+7=0

is rotated through an angle (

\frac{\pi}{4}

) in the clockwise direction about the point

(-1,1)

. The equation of the line in its new position is

Options

A $7 y+x-6=0$
B $7 y-x-6=0$
C $7 y+x+6=0$
D $7 y-x+6=0$

Correct answer

A. $7 y+x-6=0$

Step-by-step solution

(-1,1)

is a point on

3 x-4 y+7=0

, the rotation is possible. Slope of the given line

=3 / 4

. Slope of the line in its new position (=\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) \text{ or }7 \mathrm{y}+\mathrm{x}-6=0)

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