I see now. Triangle 2 is a rotated version of triangle 1. There are two ways to do this. The mathematical way or the geometric way. The geometric way is simpler and you should be able to derive the mathematical way from it. This picture illustrates my approach:
1. Draw your triangles (blue is 1, green is 2)
2. Draw a line between the corresponding points of each triangle (red lines)
3. Draw perpendicular lines through the center of each red line (yellow lines)
4. The intersection of the yellow lines is the center of rotation
Mathematically you can do the same by finding equations for all the lines and then the intersection point at the end.
The theory is this:
As the triangle's points rotate they trace out circles. The red lines represent chords of the circles. The intersection point of lines which pass through the center of the chords and are perpendicular to the chords (the yellow lines) is the center of the circle.
Hope this helps!