document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=883375>Question 883375</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you demonstrate that the perpendicular bisectors of the sides of any triangle with the points (-a,0) ; (b,c) ; (a,0) will intersect? I have tried to use the point-slope method to find the slope of each bisector, but come up with too many square roots of expressions subtracting too many variables.\r<BR>\n" );
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document.write( "English teacher trying to learn precalculus, Steve.\r<BR>\n" );
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document.write( "Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #533621 by </B><A HREF=/tutors/aboutme.mpl?userid=MathTherapy><B>MathTherapy(10555)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathTherapy><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=MathTherapy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=533621\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "How do you demonstrate that the perpendicular bisectors of the sides of any triangle with the points (-a,0) ; (b,c) ; (a,0) will intersect? I have tried to use the point-slope method to find the slope of each bisector, but come up with too many square roots of expressions subtracting too many variables.\r<BR>\n" );
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document.write( "English teacher trying to learn precalculus, Steve.\r<BR>\n" );
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document.write( "Thanks!\r<BR>\n" );
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document.write( "The perpendicular bisectors (PBs) of the sides of a triangle, with the PBs having points (- a, b), (b, c), and (a, 0) will INTERSECT INSIDE or OUTSIDE the triangle, at the CIRCUMCENTER, depending on whether the triangle is OBTUSE or ACUTE.\r<BR>\n" );
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document.write( "To prove that the PBs will intersect, let a be 5, b be 6, and c be 7. Therefore, the points (- a, b), (b, c), and (a, 0) become: (- 5, 6), (6, 7), and (5, 0), respectively. \r<BR>\n" );
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document.write( "Beginning with coordinate end-points, (- 5, 6) and (6, 7), find the coordinates of the MIDPOINT of this line. Then determine its slope. The equation to be determined will have a slope that is perpendicular to this slope. Using the coordinates of the midpoint, and the perpendicular slope, determine the equation of the perpendicular bisector of line with coordinate points (- 5, 6) and (6, 7).\r<BR>\n" );
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document.write( "Repeat the exact process with the side of the triangle having coordinate end-points: (- 5, 6) and (5, 0). \r<BR>\n" );
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document.write( "Again, repeat the exact process with the side of the triangle having coordinate end-points: (- 5, 0) and (6, 7).\r<BR>\n" );
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document.write( "Now, set two of the 3 equations equal to each other and determine the values of x and y.\r<BR>\n" );
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document.write( "Then, substitute these x and y values into the 3rd equation that WAS NOT used prior, to determine if the equation is TRUE. If the 3rd equation proves TRUE, based on the substituted x and y values, the THREE (3) equations INTERSECT at the x and y–coordinate point, just-found. Thus, the THREE (3) perpendicular bisectors of the sides of the triangle do INTERSECT, possibly INSIDE or OUTSIDE the triangle at a point called the CIRCUMCENTER.\r<BR>\n" );
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document.write( "If you’re confused by this explanation, let me know. I have created a graph on the coordinate plane to make the problem less complicated, through visualization. </SPAN>\n" );
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