document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197815>Question 1197815</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, can you solve this? with a solution and the formula to use, thankyou.<BR>\n" );
document.write( "The vertices of a triangle are at ( 4, 5 ), ( -7, -6 ) and ( 10, -3 ). Show that the line joining the midpoints of any two sides is equal to one-half of the third side. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #831243 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=831243\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Let<BR>\n" );
document.write( "A = ( 4, 5 )<BR>\n" );
document.write( "B = ( -7, -6 )<BR>\n" );
document.write( "C = ( 10, -3 )<BR>\n" );
document.write( "represent the vertices of the triangle.\r<BR>\n" );
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document.write( "Furthermore we'll have<BR>\n" );
document.write( "P = midpoint of AB<BR>\n" );
document.write( "Q = midpoint of BC<BR>\n" );
document.write( "R = midpoint of AC\r<BR>\n" );
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document.write( "Drawing:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C500%2C-12%2C12%2C-10%2C10%2C%0D%0Agraph%28500%2C500%2C-12%2C12%2C-10%2C10%2C0%29%2C%0D%0Aline%284%2C5%2C-7%2C-6%29%2C%0D%0Aline%284%2C5%2C10%2C-3%29%2C%0D%0Aline%28-7%2C-6%2C10%2C-3%29%2C%0D%0Acircle%284%2C5%2C0%29%2C%0D%0Acircle%284%2C5%2C0.1%29%2C%0D%0Acircle%284%2C5%2C0.2%29%2C%0D%0Acircle%28-7%2C-6%2C0%29%2C%0D%0Acircle%28-7%2C-6%2C0.1%29%2C%0D%0Acircle%28-7%2C-6%2C0.2%29%2C%0D%0Acircle%2810%2C-3%2C0%29%2C%0D%0Acircle%2810%2C-3%2C0.1%29%2C%0D%0Acircle%2810%2C-3%2C0.2%29%2C%0D%0Acircle%28-1.5%2C-0.5%2C0%29%2C%0D%0Acircle%28-1.5%2C-0.5%2C0.1%29%2C%0D%0Acircle%28-1.5%2C-0.5%2C0.2%29%2C%0D%0Acircle%281.5%2C-4.5%2C0%29%2C%0D%0Acircle%281.5%2C-4.5%2C0.1%29%2C%0D%0Acircle%281.5%2C-4.5%2C0.2%29%2C%0D%0Acircle%287%2C1%2C0%29%2C%0D%0Acircle%287%2C1%2C0.1%29%2C%0D%0Acircle%287%2C1%2C0.2%29%2C%0D%0Alocate%284%2C5%2B0.8%2C%22A%22%29%2C%0D%0Alocate%28-7%2C-6-0.25%2C%22B%22%29%2C%0D%0Alocate%2810%2C-3-0.25%2C%22C%22%29%2C%0D%0Alocate%28-1.5%2C-0.5-0.25%2C%22P%22%29%2C%0D%0Alocate%281.5%2C-4.5-0.25%2C%22Q%22%29%2C%0D%0Alocate%287%2C1%2B0.8%2C%22R%22%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To compute the midpoint, we add up the x coordinates and divide in half. <BR>\n" );
document.write( "Let's do this for points A(4,5) and B(-7,-6)<BR>\n" );
document.write( "Add: 4 + (-7) = -3<BR>\n" );
document.write( "Cut in half: -3/2 = -1.5<BR>\n" );
document.write( "This is the x coordinate of point P\r<BR>\n" );
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document.write( "Do the same for the y coordinates<BR>\n" );
document.write( "Add: 5 + (-6) = -1<BR>\n" );
document.write( "Cut in half: -1/2 = -0.5\r<BR>\n" );
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document.write( "Point P is located at (-1.5, -0.5)\r<BR>\n" );
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document.write( "Here's what you should get for points P through R<BR>\n" );
document.write( "P = (-1.5, -0.5)<BR>\n" );
document.write( "Q = (1.5, -4.5)<BR>\n" );
document.write( "R = (7, 1)<BR>\n" );
document.write( "I'll skip the steps showing how to locate Q and R, but you'd follow similar steps when I found P.\r<BR>\n" );
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document.write( "-----------------------------------------------------\r<BR>\n" );
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document.write( "Definition: A midsegment is a segment connecting two midpoints of a triangle.\r<BR>\n" );
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document.write( "We have these three midsegments<BR>\n" );
document.write( "PQ<BR>\n" );
document.write( "PR<BR>\n" );
document.write( "QR\r<BR>\n" );
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document.write( "Let's use the distance formula to find the distance from B(-7,-6) to C(10,-3)\r<BR>\n" );
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document.write( "(x1,y1) = (-7,-6) and (x2,y2) = (10,-3)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28+%28x1-x2%29%5E2+%2B+%28y1-y2%29%5E2+%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28+%28x1-x2%29%5E2+%2B+%28y1-y2%29%5E2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28+%28-7-10%29%5E2+%2B+%28-6-%28-3%29%29%5E2+%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28+%28-7-10%29%5E2+%2B+%28-6-%28-3%29%29%5E2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28+298+%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28+298+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Segment BC is exactly <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28298%29 ALIGN=MIDDLE  ALT=\"sqrt%28298%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > units long.\r<BR>\n" );
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document.write( "Now let's find the distance from P(-1.5, -0.5) to R(7, 1)<BR>\n" );
document.write( "(x1,y1) = (-1.5,-0.5) and (x2,y2) = (7,1)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28+%28x1-x2%29%5E2+%2B+%28y1-y2%29%5E2+%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28+%28x1-x2%29%5E2+%2B+%28y1-y2%29%5E2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28+%28-1.5-7%29%5E2+%2B+%28-0.5-1%29%5E2+%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28+%28-1.5-7%29%5E2+%2B+%28-0.5-1%29%5E2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28+74.5+%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28+74.5+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Midsegment PR is exactly <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2874.5%29 ALIGN=MIDDLE  ALT=\"sqrt%2874.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > units long.\r<BR>\n" );
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document.write( "Compute the ratio of BC and PR.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28BC%29%2F%28PR%29+=+sqrt%28+298+%29%2Fsqrt%28+74.5+%29 ALIGN=MIDDLE  ALT=\"%28BC%29%2F%28PR%29+=+sqrt%28+298+%29%2Fsqrt%28+74.5+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28BC%29%2F%28PR%29+=+sqrt%28+298%2F74.5+%29 ALIGN=MIDDLE  ALT=\"%28BC%29%2F%28PR%29+=+sqrt%28+298%2F74.5+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28BC%29%2F%28PR%29+=+sqrt%28+4+%29 ALIGN=MIDDLE  ALT=\"%28BC%29%2F%28PR%29+=+sqrt%28+4+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28BC%29%2F%28PR%29+=+2 ALIGN=MIDDLE  ALT=\"%28BC%29%2F%28PR%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We can then rearrange that like so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28BC%29%2F%28PR%29+=+2 ALIGN=MIDDLE  ALT=\"%28BC%29%2F%28PR%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC+=+2%2APR ALIGN=MIDDLE  ALT=\"BC+=+2%2APR\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PR+=+%281%2F2%29%2ABC ALIGN=MIDDLE  ALT=\"PR+=+%281%2F2%29%2ABC\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Showing us that midsegment PR is exactly half as long compared to BC.\r<BR>\n" );
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document.write( "-----------------------------------------------------\r<BR>\n" );
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document.write( "Repeat these sets of steps to show these two other facts<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PQ+=+%281%2F2%29%2AAC ALIGN=MIDDLE  ALT=\"PQ+=+%281%2F2%29%2AAC\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=QR+=+%281%2F2%29%2AAB ALIGN=MIDDLE  ALT=\"QR+=+%281%2F2%29%2AAB\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I'll let the student do these.<BR>\n" );
document.write( "</font> </SPAN>\n" );
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