The line \(3 x-4 y+7=0\) is rotated through an angle \(\frac{\pi}{4}\) in the clockwise direction about 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
\(7 y+x-6=0\)
\(7 y-x-6=0\)
\(7 y+x+6=0\)
\(7 y-x+6=0\)
Solution
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
\(\mathrm{y}-1=-\frac{1}{7}(\mathrm{x}+1) \text { or } 7 \mathrm{y}+\mathrm{x}-6=0\)