My Math Forum calculate the coordinates of the image P' of the point (3;5)

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 May 25th, 2012, 02:07 AM #1 Newbie   Joined: Mar 2012 Posts: 24 Thanks: 0 calculate the coordinates of the image P' of the point (3;5) Calculate the coordinates of the image P' of the point (3;5) after a clockwise rotation about the origin through an angle of 210 degrees.
 May 25th, 2012, 03:23 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,927 Thanks: 2205 You posted that earlier. I replied here.
 May 25th, 2012, 03:36 AM #3 Newbie   Joined: Mar 2012 Posts: 24 Thanks: 0 Re: calculate the coordinates of the image P' of the point ( o OK thank you I thought it was a reply to the glide reflection part. Thanks I got the answer but for future reference can you explain to me how to interpret which equation to use between the one you mentioned and (xcostheta + ysintheta; ycostheta-xsintheta)?
 May 25th, 2012, 03:38 AM #4 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond Re: calculate the coordinates of the image P' of the point ( $P'(x,\,y)\,=\,$$-\frac{3\sqrt{3}\,+\,5}{2},\,\frac{3\,-\,5\sqrt{3}}{2}$$$
May 25th, 2012, 03:46 AM   #5
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Quote:
 Originally Posted by joker91 . . . the one you mentioned . . .
What you gave corresponds to what I posted. What difference are you referring to? p' = Rp, where R is the rotation matrix, and p and p' are the (column) position vectors for the points P and P' respectively.

 May 25th, 2012, 03:49 AM #6 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond Re: calculate the coordinates of the image P' of the point ( Clockwise: $\begin{pmatrix} \cos{\theta}&\sin{\theta} \\ -\sin{\theta}&\cos{\theta} \end{pmatrix}$ Counterclockwise: $\begin{pmatrix} \cos{\theta}&-\sin{\theta} \\ \sin{\theta}&\cos{\theta} \end{pmatrix}$
 May 25th, 2012, 04:56 AM #7 Newbie   Joined: Mar 2012 Posts: 24 Thanks: 0 Re: calculate the coordinates of the image P' of the point ( thank you greg1313 that cleared it up and thank you skipjack for the reply

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### what is the image of point (3 5) of the rotation is -180 degrees

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