document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=992821>Question 992821</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I need help solving this : Find the point (x, y) on the line y=x that is equidistant from the points  (8, 9) and (1, -10), thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #612321 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=612321\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you want to find the point on the line y = x that is the same distance from the points (8,9) and (1,-10).\r<BR>\n" );
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document.write( "that point will be (x,y) = (22/26, 22/26)\r<BR>\n" );
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document.write( "the following graph shows you where that point lies on the graph.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/092803.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "here's how you find it.\r<BR>\n" );
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document.write( "you need to find the equation of the line between the points (8,9) and (1,-10).\r<BR>\n" );
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document.write( "the equation of that line is y = 19/7 * x - 89/7.\r<BR>\n" );
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document.write( "you then need to find  the midpoint of that line.\r<BR>\n" );
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document.write( "the midpoint of that line is (4.5, -1/2).\r<BR>\n" );
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document.write( "you then need to find the equation of a line perpendicular to the line of y = 19/7 * x - 89/7 and passing through the point (4.5, -1/2).\r<BR>\n" );
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document.write( "the equation of that line is y = -7/19 * x + 22/19.\r<BR>\n" );
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document.write( "that line is perpendicular to the line y = 19/7 * x - 89/7 because it's slope is the negative reciprocal of the slope of that line.\r<BR>\n" );
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document.write( "it doesn't look like it's perpendicular on the graph because i forgot to square the axes to make it look like what it is.\r<BR>\n" );
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document.write( "i'll correct that and show it to you again below after it's been squared.\r<BR>\n" );
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document.write( "that perpendicular line is the perpendicular bisector of the original line of y = 19/7 * x - 89/7.\r<BR>\n" );
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document.write( "any point on that line will be equidistant from the end points of that original line.\r<BR>\n" );
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document.write( "since that point needs to also intersect the line y = x, you need to find the intersection of the line y = x with the line y = -7/19 * x + 22/19.\r<BR>\n" );
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document.write( "that point is (22/26,22/26).\r<BR>\n" );
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document.write( "on the graph that shows up as .846 rounded to 3 decimal places, or .85 rounded to two decimal places.\r<BR>\n" );
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document.write( "following is the picture of the same graph after it was squared.<BR>\n" );
document.write( "this picture clearly shows the perpendicularity.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/092804.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "i calculated the distance between the point (22/26,22/26) and the points (8,9) and (1,-10) and confirmed that the distances are the same.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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