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

Question

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, $7 y+x-6=0$, $7 y-x-6=0$, $7 y+x+6=0$, $7 y-x+6=0$

MARKS App · Accepted Answer

As $(-1,1)$ 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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