document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=698437>Question 698437</A>: <I><SPAN STYLE=\"word-break: break-all;\"> segment AB with endpoints A=(-4,-6) AND b=(5,1)<BR>\n" );
document.write( "a.Find the midpoint of AB.<BR>\n" );
document.write( "b.Find the slope of the containing A and B<BR>\n" );
document.write( "c.Find AB<BR>\n" );
document.write( "please explain it step by step and how you got the answer. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #430673 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=430673\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  <BR>\n" );
document.write( "midpoint will be \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_of_segment_connecting_two_point.solver>To find midpoint of segment connecting two point</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT> The <A  rel=nofollow HREF=http://www.algebra.com/algebra/about/history/Coordinates-%2528mathematics%2529.wikipedia>Coordinates</A> of mid point of a <A  rel=nofollow HREF=line-ray-and-segments.lesson>line segment</A> joining two points can be calculated using following formulas.<BR>\n" );
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document.write( "  <b>X coordinate of mid point is</b><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X%5Bmid%5D=+%28X+coordinate_of_first_point+%2B+X+coordinate_of_first_point%29%2F2 ALIGN=MIDDLE  ALT=\"X%5Bmid%5D=+%28X+coordinate_of_first_point+%2B+X+coordinate_of_first_point%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X%5Bmid%5D+=%28-4%2B5%29%2F2 ALIGN=MIDDLE  ALT=\"X%5Bmid%5D+=%28-4%2B5%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X%5Bmid%5D+=%28-4%2B5%29%2F2=0.5 ALIGN=MIDDLE  ALT=\"X%5Bmid%5D+=%28-4%2B5%29%2F2=0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <b>Y coordinate of mid point is</b><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y%5Bmid%5D=+%28Y+coordinate_of_first_point+%2B+Y+coordinate_of_first_point%29%2F2 ALIGN=MIDDLE  ALT=\"Y%5Bmid%5D=+%28Y+coordinate_of_first_point+%2B+Y+coordinate_of_first_point%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y%5Bmid%5D+=%28-6%2B1%29%2F2 ALIGN=MIDDLE  ALT=\"Y%5Bmid%5D+=%28-6%2B1%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y%5Bmid%5D=%28-6%2B1%29%2F2=-2.5 ALIGN=MIDDLE  ALT=\"Y%5Bmid%5D=%28-6%2B1%29%2F2=-2.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Hence, The mid point of segment joining two point (-4,-6) and (5,1) is (0.5,-2.5)<BR>\n" );
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document.write( "a. the midpoint of AB is at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.5 ALIGN=MIDDLE  ALT=\"0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2.5 ALIGN=MIDDLE  ALT=\"-2.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "b.Find the slope\r<BR>\n" );
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document.write( " first find the equation of a line that passes through given points\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=find_equation_of_line.solver>FIND EQUATION of straight line given 2 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) = (-4, -6) and (x2, y2) = (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+=+%281--6%29%2F%285--4%29+=+0.777777777777778 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=0.777777777777778%2A-4+%2Bb+=+-2.88888888888889 ALIGN=MIDDLE  ALT=\"0.777777777777778%2A-4+%2Bb+=+-2.88888888888889\"   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=-6-0.777777777777778%2A-4+=+-2.88888888888889 ALIGN=MIDDLE  ALT=\"b=-6-0.777777777777778%2A-4+=+-2.88888888888889\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  y=(0.777777777777778)x + (-2.88888888888889)<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%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0A++++graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+0.777777777777778%2Ax%2B-2.88888888888889+%29%2C%0D%0A++++red%28+locate%28+-4%2C+-6%2C+%22-4%2C+-6%22+%29%2C+circle%28+-4%2C+-6%2C+0.15+%29+%29%2C%0D%0A++++green%28+locate%28+5%2C+1%2C+%225%2C+1%22+%29%2C+circle%28+5%2C+1%2C+0.15+%29+%29%0D%0A++%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "the slope is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=0.777777777777778 ALIGN=MIDDLE  ALT=\"m=0.777777777777778\"   DISABLED_style= \"max-width:90%; height:auto;\" > or rounded <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=0.8 ALIGN=MIDDLE  ALT=\"m=0.8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "c.Find AB\r<BR>\n" );
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document.write( "first find the distance between <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B ALIGN=MIDDLE  ALT=\"B\"   DISABLED_style= \"max-width:90%; height:auto;\" >, it will be answer to c\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=hummingbird_distance_2D.solver>Distance between two points in two dimensions</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>The distance (denoted by d) between two points in two dimensions is given by the following formula:<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;\" ><BR>\n" );
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document.write( "  Thus in our case, the required distance is<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%28%28-4-5%29%5E2+%2B+%28-6-1%29%5E2%29=+11.4017542509914+ ALIGN=MIDDLE  ALT=\"d=sqrt%28%28-4-5%29%5E2+%2B+%28-6-1%29%5E2%29=+11.4017542509914+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
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document.write( "  For more on this concept, refer to <A  rel=nofollow HREF=Distance_formula.wikipedia>Distance formula</A>.<BR>\n" );
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document.write( "so, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB=11.4 ALIGN=MIDDLE  ALT=\"AB=11.4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );