document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1118318>Question 1118318</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all the points having an x-coordinate of 9 whose distance from the point (3, -2) is 10.<BR>\n" );
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document.write( "(9, 13), (9, -7)<BR>\n" );
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document.write( "(9, 2), (9, -4)<BR>\n" );
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document.write( "(9, 6), (9, -10)<BR>\n" );
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document.write( "(9, -12), (9, 8)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #733623 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=733623\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The formal algebraic solution method which has you finding the answer by solving a quadratic equation is of course valid.  But the problem can be made much easier than that.<br><BR>\n" );
document.write( "You are looking for the two points on the line x=9 whose distance from (3,-2) is 10.<br><BR>\n" );
document.write( "The horizontal distance from (3,-2) to the line x=9 is 9-3 = 6.  So that horizontal line segment, the line x=9, and the segments from (3,-2) to the points we are looking for will form two right triangles, each with one leg 6 and hypotenuse 10.<br><BR>\n" );
document.write( "Quick use of the Pythagorean Theorem (or the recognition that 6-8-10 is a multiple of the common 3-4-5 right triangle) make the other leg of each right triangle 8.<br><BR>\n" );
document.write( "Then the two points on the line x=9 that are 8 units from y=-2 are -2+8 = 6 and -2 -8 = -10.<br><BR>\n" );
document.write( "So the two points we are looking for are (9,-10) and (9,6). </SPAN>\n" );
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