Find the centre of rotation?

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1 Answer
Mar 5, 2018

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:

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