# Math Help - Rotate a line about a point

1. ## Rotate a line about a point

Hi

I have a line with end points (x1,y1) and (x2,y2). If I rotate a line about the point (x3,y3) at an angle 'a', it wlll be parallel to x axis. At what angle should I rotate the line about another point (x4,y4), to make it parallel to the x axis?

Is there any formula for calculating the angle for rotating the line about the point (x4,y4)?

Manu

2. Originally Posted by ManuLi
Hi

I have a line with end points (x1,y1) and (x2,y2). If I rotate a line about the point (x3,y3) at an angle 'a', it wlll be parallel to x axis. At what angle should I rotate the line about another point (x4,y4), to make it parallel to the x axis?

Is there any formula for calculating the angle for rotating the line about the point (x4,y4)?

Manu
1. Do you mean maybe
At what angle should I rotate the line about another point (x4,y4), to make it parallel to the y axis?
2. If not: If the line isn't parallel to the x-axis and you know one specific angle a which produces a parallel to the x-axis then any arbitrary point will serve as center of the rotation. You'll get a parallel to the x-axis, only the place, where this parallel will be, is changing.

The line has the endpoints A and B;
the red point $P_1$ produces a parallel line to the x-axis (drawn in red)
an the blue point $P_2$ produces a parallel line to the x-axis different from the first parallel.

As you can see your angle a has the same value (but the opposite direction) as the angle formed by the original line and a parallel to the x-axis.