How do you find the centre of rotation?

Method 1

1. Draw a line between the corresponding points
2. Construct the perpendicular bisect of these points
3. Do this for each point until they cross
4. That is your centre of rotation

It sounds complicated but when you see these examples you will find it easy.

Example 1

Find the centre of rotation

Connect both A corners up

Draw a line between the corresponding points

Now bisect the line.

Bisect the connection through 90 degrees

Now do the same for another point.

Join the other corners and bisect like corners A

Centre of rotation = (1,0).

Method 2

Use logic

Because the centre of rotation is the same distance away from corresponding points.

Example

Find the centre of rotation using logic

Ask: What point is the same distance from `A` to `A^1` that would cause this rotation.

Is it (0,1)..................... No

(0,0)..................... No

(1,1)..................... No

(1,0)..................... Yes

It has to be (1,0)

But now check the other corners.

Draw A and D corners to the x axis, they meet at 1

Is `D` to centre and `D^1` to centre the same distance?

The answer is YES

You can see that the answer would be yes for `B` to centre and `B^1` to centre, as well as `C` to centre and `C^1` to centre.

So YES (0,1) is the centre.