Question

Find the centre of rotation?

Answer 1

The centre of rotation is `(–1, " "2).`

Explanation:

Figure `A` has been rotated 90° counter-clockwise to figure `B.` Pick one point on figure `A` and find its matching point in `B.`

I'll pick `P=(2,–2)` and its corresponding point `P^star=(3,5).`

Measure the vertical distance between these two points. Go from `B` to `A.`

My vertical distance is `5-(–2)=7`.

Measure the horizontal difference between them too, but this time, go from `A` to `B.`

My horizontal distance is `2-3=–1`.

Split the vertical difference `(7)` into the sum of two numbers that differ by the horizontal distance `(–1).`

My two numbers will be `3` and `4` in that order, since `3-4=–1.`

The centre of rotation will be `3` left and `4` up from our point in `A,` which puts it at

`color(white)= (2-3, "  "–2+4)`
`=(–1,"  "2)`.

We can see this is the centre of rotation because we can draw a `3xx4` rectangle with one corner at `(–1," "2)` and the other corner at either `P` or `P^star:`