document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1164197>Question 1164197</A>: <I><SPAN STYLE=\"word-break: break-all;\">  A half-turn centered at (−3,4) is applied to (−5,1). Find coordinates for the image point. What are the coordinates when the half-turn centered at (a, b) is applied to (x, y)?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #788678 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13215)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=788678\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "A half turn centered about A, applied to B, results in an image C where A is the midpoint of BC.<br><BR>\n" );
document.write( "For the general case (your second question), a half turn centered at (a,b) applied to (x,y) will produce an image at (a+(a-x),b+(b-y)), or (2a-x,2b-y).<br><BR>\n" );
document.write( "To get some learning from this problem, it would be good to solve the first of your problems in two different ways, to see that the answers are the same: (1) by using the idea of (-3,4) as the midpoint of the line segment; and (2) by using the general formula.<br><BR>\n" );
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