I am lost to figure out where would be the centre of rotation of triangle #1 to Traingle #2..
No idea where to start..
Any one please help me? Or show me a direction?
Ex. Triangle #1 has these coordinates: (3,4), (7,4), (3,7)
Triangle #2 has these coordinates: (3,2), (6,2), (3,-2)

Thanks!

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:
Attachment 3192

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!

Perfect! Thanks a mill.
Iam not sure though which lines you are talking about to find equations for.

you can find the equations for the red lines first, then the yellow lines from those, then the center of the circle from the yellow line intersections. I can help with this if you need.

I can find equations for the red lines no problem, but then how do u find equations for the perpendicular yellow lines? Just give me a hint. Actually need to find equations just for 2 lines to get the intersection.
Thanks again!

Yep. So you know that the yellow lines go through the middle of the red lines. You can find the mid point of the line?
Then it has to be perpendicular to the red line so the slope of the yellow line needs to be the negative reciprocal of the red line's slope. So if the red line's slope is m the yellow line's slope is -1/m.
Just do this for 2 red lines, then find the intersection of those two yellow lines.

How do you find the mid point?

The midpoint x val is just the average of the two points x values and the midpoint y val is the average of the two points y values.

so:


does that make sense?

Yes very much !
Thanks!