document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1139586>Question 1139586</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find y if the distance between points p and R is 25 and point R is located in the first quadrant.\r<BR>\n" );
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document.write( "P=(3,-8)<BR>\n" );
document.write( "R=(10,y) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #760080 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=760080\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> point p is at (3,-8)<BR>\n" );
document.write( "point r is at (10,y)\r<BR>\n" );
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document.write( "the distance between them is 25.\r<BR>\n" );
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document.write( "point r is in the first quadrant.\r<BR>\n" );
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document.write( "this means that y has to be positive.\r<BR>\n" );
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document.write( "the distance between point p and point r is equal to sqrt((y+8)^2 + (10-3)^2).\r<BR>\n" );
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document.write( "simplify this to get distance between points p and r is equal to sqrt((y+8)^2 + 49)\r<BR>\n" );
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document.write( "since the distance between points p and r is 25, then the formula becomes:\r<BR>\n" );
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document.write( "25 = sqrt((y+8)^2 + 49)\r<BR>\n" );
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document.write( "square both sides of the equation to get 625 = (y+8)^2 + 49\r<BR>\n" );
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document.write( "simplify to get 625 = y^2 + 16y + 64 + 49\r<BR>\n" );
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document.write( "combine like terms to get 625 = y^2 + 16y + 113\r<BR>\n" );
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document.write( "subtract 625 from both sides of the equation to get 0 = y^2 + 16y - 512.\r<BR>\n" );
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document.write( "factor this quadratic equation to get (y + 32) * (y - 16) = 0\r<BR>\n" );
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document.write( "solve for y to get y = -32 or 16.\r<BR>\n" );
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document.write( "y is positive, so y has to be 16.\r<BR>\n" );
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document.write( "your solution is that y = 16.\r<BR>\n" );
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document.write( "this means that point p = (3,-8) and point r = (10,16)\r<BR>\n" );
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document.write( "the distance between points p and r is equal to sqrt((16+8)^2 + (10-3)^2).\r<BR>\n" );
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document.write( "that becomes equal to sqrt((24)^2 + 7^2) which becomes equal to sqrt(625) which becomes equal to 25.\r<BR>\n" );
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document.write( "that confirms that, when y = 16, the distance between p and r is 25.\r<BR>\n" );
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document.write( "the equation of the line between points p and r is y = 24/7 * x -128/7.\r<BR>\n" );
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document.write( "the graph of that equation is shown below.\r<BR>\n" );
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document.write( "it shows that the points (3,-8) and (10,16) are both on the line, as they sh ould be.\r<BR>\n" );
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