# Rotation Transformation - find center

• Mar 26th 2011, 11:50 PM
mathguy80
Rotation Transformation - find center
Hi,

This is a rotation transform problem, that I am struggling with.

The vertices of Triangle ABC are A(1,1), B(2, 2), and C(0,3). The vertices of Triangle A1B1C1 are A1(-2, 2), B1(-3,3), and C1(-4, 1). Describe fully the single transformation which maps Triangle ABC onto A1B1C1.

http://i.imgur.com/UjTpX.png

I can make out that it is a rotation of 90 degrees anti-clockwise. But what is the center of the rotation. How do you find the center of rotation for such transformations where the center is not origin. Thanks for your help!

P.S. Ignore the small letters, haven't figured out how to hide those yet!
• Mar 27th 2011, 02:21 AM
earboth
Quote:

Originally Posted by mathguy80
Hi,

This is a rotation transform problem, that I am struggling with.

The vertices of Triangle ABC are A(1,1), B(2, 2), and C(0,3). The vertices of Triangle A1B1C1 are A1(-2, 2), B1(-3,3), and C1(-4, 1). Describe fully the single transformation which maps Triangle ABC onto A1B1C1.

I can make out that it is a rotation of 90 degrees anti-clockwise. But what is the center of the rotation. How do you find the center of rotation for such transformations where the center is not origin. Thanks for your help!

P.S. Ignore the small letters, haven't figured out how to hide those yet!

1. Determine the perpendicular bisectors of AA' and BB'.

2. The point of intersection of these two bisectors is the center of the rotation. You should come out with C(-1, 0)
• Mar 27th 2011, 02:59 AM
mathguy80
Sweet! Perpendicular bisector of chord of a circle passes through it's center! @earboth to the rescue once again. :)
• Apr 18th 2012, 12:33 PM
JOMath
Re: Rotation Transformation - find center
Sorry for a newcomer to bump an old thread, but my daughter was struggling with just this problem for her homework tonight and Google found this as an answer. The terminology baffled me a bit until she recalled bisecting a line with a compass. We printed the homework page, and used the pencil compass to find the half way lines between the two points. It was brilliant that where they intersected could clearly be seen as the rotation point. I knew there would be a failsafe method of finding it. Earboth - thank you very much - I even get the bit about why it works. :-)