How do I find the center of rotation between two rectangles?

Question

B(-1,1),C(-1,3),D(-5,3), and E(-5,1) are the vertices of the preimage on the coordinate plane. B'(-1,-3),C'(-3,-3),D'(-3,-7), and E'(-1,-7) are the vertices of the after image on the same coordinate plane. Rectangle B'C'D'E' can be considered the rotation image of BCDE, the camera should be located at the center of rotation. Using only a compass and a straightedge, find the point where the camera should be located. Name this point A.

Answer 1

To rotate a two dimension image, you need to put you camera in third dimension.

Put a perpendicular on both of rectangles (centers of rectangles) and project them to intersect. Intersection point would be Camera Point A.

Answer 2

What you want is a point that is simultaneously equidistant from B and B' as well as C and C' as well as D and D' and finally E and E'. This point must be long the y = -1 line in order to lie equidistant from B and B'. Usuing any other point to find the x coordinate, I came to the conclusion that A is (1,-1).
The test is, using the compass, make a circle, using A as the center, and the radius AB. If it passes through AB', it works. Repeat for AC, AD and AE.

Answer 3

The rotation maps B on to B', C onto C', D onto D' and E onto E'. Therefore BB', CC', DD' and EE' are chords of the same circle.

To find the centre, draw the chords and find the perpendicular bisector of each one. The bisectors will all intersect in the same point. The point of intersection is the centre of the rotation.