# Thread: equation of line by rotation

1. ## equation of line by rotation

Find the equation of the line obtained by the rotation of the line x + y − 4 = 0 by pi/4

2. Rotated about any particular point ?

3. sorry, forgot to mention by pi/4 around the origin counter-clockwise

4. $x+y-4=0\Rightarrow\ y=-x+4$

which means the line has an angle of $-\frac{\pi}{4}$
relative to the positive side of the x-axis.

However, it does not go through the origin as $(0,4)$ is on the line.

The rotated line can pass through the origin, if we write the rotated line as $y=mx+c$, finding "m" and setting $c=0$

Is that what you are looking for ?

5. We could take a point on the line and rotate the line at that point.
We could rotate "around" the origin if the line is a tangent to the circle $x^2+y^2=8$
since the given line is a tangent to that circle.

We need clarification.