document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=742526>Question 742526</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Indicate the equation of the given line in standard form.\r<BR>\n" );
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document.write( "The line containing the median of the trapezoid whose vertices are R(-1, 5) , S(1, 8), T(7, -2), and U(2, 0). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #452523 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=452523\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28600%2C600%2C-10%2C10%2C-10%2C10%2Cgrid%281%29%2Cline%28+0%2C+6.5%2C+4.5%2C+-1+%29%2Ccircle%280%2C6.5%2C0.2%29%2Ccircle%284.5%2C-1%2C0.2%29%2Cline%28+-1%2C+5%2C+2%2C+0+%29%2Cline%28+2%2C+0%2C+7%2C+-2+%29%2Cline%28+-1%2C+5%2C+1%2C+8+%29%2Cline%281%2C+8%2C+7%2C+-2+%29%2Ccircle%282%2C0%2C0.2%29%2Clocate%282.3%2C0.5%2C%22U%282%2C0%29%22%29%2Ccircle%287%2C-2%2C0.2%29%2Clocate%287.5%2C-2.5%2C%22T%287%2C-2%29%22%29%2Ccircle%281%2C8%2C0.2%29%2Clocate%281.5%2C8.5%2C%22S%281%2C8%29%22%29%2Ccircle%28-1%2C5%2C0.2%29%2Clocate%28-1.8%2C5.5%2C%22R%28-1%2C5%29%22%29%2Cgraph%28600%2C600%2C-10%2C10%2C-10%2C10%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "first draw the median of the trapezoid; find endpoints:\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=midpoint.solver>Midpoint</A></TD></TR>\n" );
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document.write( "  The first point is (x1,y1). The second point is (x2,y2)<BR>\n" );
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document.write( "  Since the first point is (-1, 5), we can say (x1, y1) = (-1, 5)<BR>\n" );
document.write( "  So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+-1 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D+=+5 ALIGN=MIDDLE  ALT=\"y%5B1%5D+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Since the second point is (1, 8), we can also say (x2, y2) = (1, 8)<BR>\n" );
document.write( "  So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+1 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D+=+8 ALIGN=MIDDLE  ALT=\"y%5B2%5D+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  Put this all together to get:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+-1 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D+=+5 ALIGN=MIDDLE  ALT=\"y%5B1%5D+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+1 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D+=+8 ALIGN=MIDDLE  ALT=\"y%5B2%5D+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Finding the x coordinate of the midpoint: Add up the corresponding x coordinates x1 and x2 and divide that sum by 2<BR>\n" );
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document.write( "  X Coordinate of Midpoint = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5B1%5D%2Bx%5B2%5D%29%2F2 ALIGN=MIDDLE  ALT=\"%28x%5B1%5D%2Bx%5B2%5D%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  X Coordinate of Midpoint = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2B1%29%2F2 ALIGN=MIDDLE  ALT=\"%28-1%2B1%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  X Coordinate of Midpoint = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2F2 ALIGN=MIDDLE  ALT=\"0%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  X Coordinate of Midpoint = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  So the x coordinate of the midpoint is 0<BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  Finding the y coordinate of the midpoint: Add up the corresponding y coordinates y1 and y2 and divide that sum by 2<BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  Y Coordinate of Midpoint = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5B1%5D%2By%5B2%5D%29%2F2 ALIGN=MIDDLE  ALT=\"%28y%5B1%5D%2By%5B2%5D%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  Y Coordinate of Midpoint = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2B8%29%2F2 ALIGN=MIDDLE  ALT=\"%285%2B8%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  Y Coordinate of Midpoint = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2F2 ALIGN=MIDDLE  ALT=\"13%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  Y Coordinate of Midpoint = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6.5 ALIGN=MIDDLE  ALT=\"6.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  So the y coordinate of the midpoint is 6.5<BR>\n" );
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document.write( "  ===============================================================================<BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  Summary:<BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  The midpoint of the segment joining the two points (-1, 5) and (1, 8) is (0, 6.5).<BR>\n" );
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document.write( "  So the answer is (0, 6.5)<BR>\n" );
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document.write( "  </TD></TR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=midpoint.solver>Midpoint</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  The first point is (x1,y1). The second point is (x2,y2)<BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  Since the first point is (2, 0), we can say (x1, y1) = (2, 0)<BR>\n" );
document.write( "  So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+2 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D+=+0 ALIGN=MIDDLE  ALT=\"y%5B1%5D+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Since the second point is (7, -2), we can also say (x2, y2) = (7, -2)<BR>\n" );
document.write( "  So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+7 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D+=+-2 ALIGN=MIDDLE  ALT=\"y%5B2%5D+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Put this all together to get:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+2 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D+=+0 ALIGN=MIDDLE  ALT=\"y%5B1%5D+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+7 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D+=+-2 ALIGN=MIDDLE  ALT=\"y%5B2%5D+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  ----------------------------------------------------------------------------------------<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Finding the x coordinate of the midpoint: Add up the corresponding x coordinates x1 and x2 and divide that sum by 2<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  X Coordinate of Midpoint = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5B1%5D%2Bx%5B2%5D%29%2F2 ALIGN=MIDDLE  ALT=\"%28x%5B1%5D%2Bx%5B2%5D%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  X Coordinate of Midpoint = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2B7%29%2F2 ALIGN=MIDDLE  ALT=\"%282%2B7%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  X Coordinate of Midpoint = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F2 ALIGN=MIDDLE  ALT=\"9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  X Coordinate of Midpoint = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.5 ALIGN=MIDDLE  ALT=\"4.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  So the x coordinate of the midpoint is 4.5<BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Finding the y coordinate of the midpoint: Add up the corresponding y coordinates y1 and y2 and divide that sum by 2<BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  Y Coordinate of Midpoint = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5B1%5D%2By%5B2%5D%29%2F2 ALIGN=MIDDLE  ALT=\"%28y%5B1%5D%2By%5B2%5D%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Y Coordinate of Midpoint = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280%2B-2%29%2F2 ALIGN=MIDDLE  ALT=\"%280%2B-2%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Y Coordinate of Midpoint = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F2 ALIGN=MIDDLE  ALT=\"-2%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Y Coordinate of Midpoint = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  So the y coordinate of the midpoint is -1<BR>\n" );
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document.write( "  ===============================================================================<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Summary:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  The midpoint of the segment joining the two points (2, 0) and (7, -2) is (4.5, -1).<BR>\n" );
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document.write( "  So the answer is (4.5, -1)<BR>\n" );
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document.write( "  </TD></TR>\n" );
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document.write( "so, endpoints are: (0, 6.5) and (4.5, -1)\r<BR>\n" );
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document.write( "now find the equation of a line containing the median of the trapezoid\r<BR>\n" );
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document.write( "<TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=change_this_name10094.solver>Find the equation of line going through points</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (0, 6.5) and (x2, y2) = (4.5, -1).<BR>\n" );
document.write( "  Slope a is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29+=+%28-1-6.5%29%2F%284.5-0%29+=+-1.66666666666667 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  Intercept is found from equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Ax%5B1%5D%2Bb+=+y%5B1%5D ALIGN=MIDDLE  ALT=\"a%2Ax%5B1%5D%2Bb+=+y%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1.66666666666667%2A0+%2Bb+=+6.5 ALIGN=MIDDLE  ALT=\"-1.66666666666667%2A0+%2Bb+=+6.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. From that, <BR>\n" );
document.write( "  intercept b is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=y%5B1%5D-a%2Ax%5B1%5D ALIGN=MIDDLE  ALT=\"b=y%5B1%5D-a%2Ax%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=6.5--1.66666666666667%2A0+=+6.5 ALIGN=MIDDLE  ALT=\"b=6.5--1.66666666666667%2A0+=+6.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  y=(-1.66666666666667)x + (6.5)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Your graph:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A++drawing%28600%2C+600%2C+-30%2C+30%2C+-30%2C+30%2C%0D%0A++++graph%28+600%2C+600%2C+-30%2C+30%2C+-30%2C+30%2C+-1.66666666666667%2Ax%2B6.5+%29%2C%0D%0A++++red%28+locate%28+0%2C+6.5%2C+%220%2C+6.5%22+%29%2C+circle%28+0%2C+6.5%2C+0.15+%29+%29%2C%0D%0A++++green%28+locate%28+4.5%2C+-1%2C+%224.5%2C+-1%22+%29%2C+circle%28+4.5%2C+-1%2C+0.15+%29+%29%0D%0A++%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  </TD></TR>\n" );
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document.write( "all together:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28600%2C600%2C-10%2C10%2C-10%2C10%2Cgrid%281%29%2Cline%28+0%2C+6.5%2C+4.5%2C+-1+%29%2Ccircle%280%2C6.5%2C0.2%29%2Ccircle%284.5%2C-1%2C0.2%29%2Cline%28+-1%2C+5%2C+2%2C+0+%29%2Cline%28+2%2C+0%2C+7%2C+-2+%29%2Cline%28+-1%2C+5%2C+1%2C+8+%29%2Cline%281%2C+8%2C+7%2C+-2+%29%2Ccircle%282%2C0%2C0.2%29%2Clocate%282.3%2C0.5%2C%22U%282%2C0%29%22%29%2Ccircle%287%2C-2%2C0.2%29%2Clocate%287.5%2C-2.5%2C%22T%287%2C-2%29%22%29%2Ccircle%281%2C8%2C0.2%29%2Clocate%281.5%2C8.5%2C%22S%281%2C8%29%22%29%2Ccircle%28-1%2C5%2C0.2%29%2Clocate%28-1.8%2C5.5%2C%22R%28-1%2C5%29%22%29%2Cgraph%28600%2C600%2C-10%2C10%2C-10%2C10%2C-1.66666666666667x%2B6.5%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "and, the equation of a line in standard form is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.66666666666667x%2By=+6.5 ALIGN=MIDDLE  ALT=\"1.66666666666667x%2By=+6.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );