document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=165289>Question 165289</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780078738265/algebrahomeworkh>Geometry</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Given: triangle ABC with coordinates A(0,0);B(a,0); and C(b,c). S is the midpoint of AC and T is the midpoint of BC. <BR>\n" );
document.write( "Prove ST=1/2 AB </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #121864 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=121864\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> given:<BR>\n" );
document.write( "point S is midpoint of AC<BR>\n" );
document.write( "point T is midpoint of BC<BR>\n" );
document.write( "point A = (0,0)<BR>\n" );
document.write( "point C = (b,c)<BR>\n" );
document.write( "point B = (a,0)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "formula for coordinates of midpoint of a line is ((x1+x2)/2,(y1+y2)/2)<BR>\n" );
document.write( "let point A = (x1,y1) = (0,0)<BR>\n" );
document.write( "x1 = 0<BR>\n" );
document.write( "y1 = 0<BR>\n" );
document.write( "let point C = (x2,y2) = (b,c)<BR>\n" );
document.write( "x2 = b<BR>\n" );
document.write( "y2 = c<BR>\n" );
document.write( "formula for midpoint of AB is (b/2,c/2) = point S.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "formula for coordinates of midpoint of a line is ((x1+x2)/2,(y1+y2)/2)<BR>\n" );
document.write( "let point B = (x1,y1) = (a,0)<BR>\n" );
document.write( "x1 = a<BR>\n" );
document.write( "y1 = 0<BR>\n" );
document.write( "let point C = (x2,y2) = (b,c)<BR>\n" );
document.write( "x2 = b<BR>\n" );
document.write( "y2 = c<BR>\n" );
document.write( "formula for midpoint of BC = ((a+b)/2,c/2) = point T.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "formula for length of a line is sqrt[(x2-x1)^2 + (y2-y1)^2]<BR>\n" );
document.write( "let point S be (x1,y1) = (b/2,c/2)<BR>\n" );
document.write( "let point T be (x2,y2) = (a+b)/2,c/2)<BR>\n" );
document.write( "length of ST = sqrt[(x2-x1)^2 + (y2-y1)^2]<BR>\n" );
document.write( "length of ST = sqrt [ ( (a+b)/2 - b/2 )^2 + ( c/2 - c/2 )^2 ]<BR>\n" );
document.write( "length of ST = sqrt [ ( (a+b-b)/2 )^2 + 0^2 ]<BR>\n" );
document.write( "length of ST = sqrt [ ( a/2 )^2 ]<BR>\n" );
document.write( "length of ST = sqrt [ ( a^2/4 ) ]<BR>\n" );
document.write( "length of ST = sqrt (a^2) / sqrt (4)<BR>\n" );
document.write( "length of ST = a/2<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "point A = (0,0)<BR>\n" );
document.write( "point B = (a,0)<BR>\n" );
document.write( "let point A = (x1,y1) = (0,0)<BR>\n" );
document.write( "let point B = (x2,y2) = (a,0)<BR>\n" );
document.write( "formula for length of a line is sqrt[(x2-x1)^2 + (y2-y1)^2]<BR>\n" );
document.write( "length of line AB = sqrt [ (a-0)^2 + (0-0)^2 ]<BR>\n" );
document.write( "length of line AB = sqrt [  a^2 + (0)^2 ]<BR>\n" );
document.write( "length of line AB = sqrt [ a^2 ]<BR>\n" );
document.write( "length of line AB = a<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "length of ST = a/2 = (1/2)*a<BR>\n" );
document.write( "length of AB = a<BR>\n" );
document.write( "length of ST = 1/2 * length of AB </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );