The line $2x-y=5$ turns about a point.... The line $2x-y=5$ turns about a point on it, whose ordinate and abscissae are equal, through an angle of $45°$, in anti clockwise direction. Find the equation of line in the new position.
My attempt to solve:
Let AB be the line with the equation $2x-y=5$ and $B(a,a)$ be a point on it whose ordinate and abscissae are equal. Then
$$2x-y=5$$
$$2a-a=5$$
$$a=5$$
Hence, $B(a,a)=B(5,5)$.
My solution ends up here. What should I do next?

The line turns by an angle of $45°$ anti-clockwise about the point $(5,5)$. Thus, you need to find the equation of a line whose angle with the $x-axis$ is $45°$ more than this line and which passes through the point $(5,5)$.
The line $2x-y=5$ has a slope of $2$, i.e., it makes an angle of $\arctan2$ with the $x-axis$.
Slope of the required line=$\tan(\frac\pi4+\arctan2)=\frac{1+2}{1-2}=-3$
Its equation, therefore, is
$$y-5=-3(x-5)$$
or
$$3x+y=20$$
