Question

The line $3x-4y+7=0$ is rotated about a point on it, whose ordinate and abscissa are equal, through an angle ${30}^o$. Find the equation of the line is new position.

Answer 1

Line $3x-4y+7=0$ is rotated by $30°$

New equation will be $3\left(x\cos 30°\right)-4\left(y\sin 30°\right)+7=0$

$=\frac{3\sqrt{3}x}{2}-2y+7=0$

$=3\sqrt{3}x-4y+14=0$

Hence, this is the answer.