document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1112319>Question 1112319</A>: <I><SPAN STYLE=\"word-break: break-all;\"> FInd the equation of the perpendicular bisector of the interval AB, where A(-3, 4) and B (5, 2). Answer in general form  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #727331 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=727331\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the points are A (-3,4) and <BR>\n" );
document.write( "B (5,2).\r<BR>\n" );
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document.write( "the slope of this line is (y2 - y1) / (x2 - x1), where (x1,y1) = (-3,4)and (x2,y2) = (5,2).\r<BR>\n" );
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document.write( "the slope is therefore (2-4) / (5-(-3)) = -2/8 = -1/4\r<BR>\n" );
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document.write( "the equation of the line, in slope intercept form, would be y = mx + b.\r<BR>\n" );
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document.write( "m is the slope.<BR>\n" );
document.write( "b is the y-intercept.\r<BR>\n" );
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document.write( "replace m with -1/4 and the equation becomes y = -1/4 * x + b\r<BR>\n" );
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document.write( "replace x and y with the value of one of the points that the line goes through and the equation becomes:\r<BR>\n" );
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document.write( "2 = -1/4 * 5 + b, if using (5,2)\r<BR>\n" );
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document.write( "solve for b to get:\r<BR>\n" );
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document.write( "b = 2 + 1/4 * 5, resulting in b = 3.25\r<BR>\n" );
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document.write( "the equation becomes y = -1/4 * x + 3.25\r<BR>\n" );
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document.write( "here's the graph, showing it going through all the points that were given and calculated algebraically.\r<BR>\n" );
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document.write( "the graph shows the x-intercept as well as the y-intercept.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/031501.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the line segment starts at (-4,3) and ends at (5,2).\r<BR>\n" );
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document.write( "the midpoint of this line seqment will be h = ((x1+x2)/2,(y1+y2)/2), where h represents the midpoint.\r<BR>\n" );
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document.write( "replace (x1,x2) with (-3,4) and (x2,y2) with (5,2) and the equation becomes ((-3+5)/2,(4+2)/2).\r<BR>\n" );
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document.write( "this results in h = (1,3).\r<BR>\n" );
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document.write( "the slope of the line perpendicular to the original line will have a slope that is a negative reciprocal of the original line.\r<BR>\n" );
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document.write( "the slope of the original line is -1/4.\r<BR>\n" );
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document.write( "the slope of the line perpendicular to it will be 4.\r<BR>\n" );
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document.write( "the slope intercept form of the perpendicular equation will be y = 4x + b.\r<BR>\n" );
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document.write( "replace (x,y) with (1,3) and the equation becomes:\r<BR>\n" );
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document.write( "3 = 4*1 + b\r<BR>\n" );
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document.write( "solve for b to get:\r<BR>\n" );
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document.write( "b = -1\r<BR>\n" );
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document.write( "the equation of the perpendicular line going through the point (1,3) is y = 4x -1\r<BR>\n" );
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document.write( "here's the graph of the perpendicular line and the original line.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/031502.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the line is perpendicular because its slope is a negative reciprocal of the original line.\r<BR>\n" );
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document.write( "the line is a bisector because the length of the line segments to the left of the point of intersection and the right of the point of intersection are congruent.\r<BR>\n" );
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document.write( "the formula for the length of a line is k = sqrt((x2-x1)^2 + (y2-y1)^2), where k represents the length of the line (the variable name is chosen arbitrarily and can be any variable name that isn't currently used in the equation).\r<BR>\n" );
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document.write( "the length of the line segment between (-3,4) and (1,3) is equal to sqrt((1-(-3))^2 + (3-4)^2) which becomes sqrt((4)^2 + (-1)^2) which becomes sqrt(16+1) which is equal to sqrt(17).\r<BR>\n" );
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document.write( "the length of the line segment between (1,3) and (5,2) is equal to sqrt((5-1)^2 + (2-3)^2) which becomes sqrt((4)^2 + (-1)^2) which becomes sqrt(16+1) which is equal to sqrt(17).\r<BR>\n" );
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document.write( "the lengths of the line segments are equal, therefore the point (1,3) is a bisector of the line between (-3,4) and (5,2).\r<BR>\n" );
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document.write( " </SPAN>\n" );
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