# 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**

Draw a line between the corresponding points

Now bisect the line.

Now do the same for another point.

Centre of rotation = (1,0).

## Method 2

Use logic

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

**Example**

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.

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.

# 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**

Draw a line between the corresponding points

Now bisect the line.

Now do the same for another point.

Centre of rotation = (1,0).

## Method 2

Use logic

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

**Example**

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.

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 fo `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.