document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=598070>Question 598070</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The point (5,y) is five units away from the point (2,70). What are the two possible values of y? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #378507 by </B><A HREF=/tutors/aboutme.mpl?userid=math-vortex><B>math-vortex(648)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math-vortex><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=math-vortex><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=378507\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, there--<BR>\n" );
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document.write( "Use the distance formula to find the distance between two points. The two different values of y will give you a point above and and a point below (2,70). <BR>\n" );
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document.write( "The distance formula is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=sqrt%28%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2%29 ALIGN=MIDDLE  ALT=\"D=sqrt%28%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Let (x[1],y[1])=(2,70).<BR>\n" );
document.write( "Let (x[2],y[2])=(5,y).<BR>\n" );
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document.write( "Substitute 5 for D and the known values for each point.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=sqrt%28%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2%29 ALIGN=MIDDLE  ALT=\"D=sqrt%28%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5=sqrt%28%285-2%29%5E2%2B%28y-70%29%5E2%29 ALIGN=MIDDLE  ALT=\"5=sqrt%28%285-2%29%5E2%2B%28y-70%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Simplify and solve for y.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5=sqrt%28%283%29%5E2%2B%28y-70%29%5E2%29 ALIGN=MIDDLE  ALT=\"5=sqrt%28%283%29%5E2%2B%28y-70%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5=sqrt%289%2By%5E2-140y%2B4900%29 ALIGN=MIDDLE  ALT=\"5=sqrt%289%2By%5E2-140y%2B4900%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5=sqrt%28y%5E2-140y%2B4909%29 ALIGN=MIDDLE  ALT=\"5=sqrt%28y%5E2-140y%2B4909%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Square both sides of the equation to clear the square root.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25=y%5E2-140y%2B4909 ALIGN=MIDDLE  ALT=\"25=y%5E2-140y%2B4909\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Set the polynomial equal to zero, and factor.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-140y%2B4884=0 ALIGN=MIDDLE  ALT=\"y%5E2-140y%2B4884=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We can use the quadratic formula or the factoring method to solve. 4884 looks like a friendly number to I would try to factor it.<BR>\n" );
document.write( " If I can't find factors right away, I switch to the quadratic formula. The Q.F. works for every quadratic, but not every quadratic is factorable.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=484=2%5E2%2A3%2A11%2A37 ALIGN=MIDDLE  ALT=\"484=2%5E2%2A3%2A11%2A37\"   DISABLED_style= \"max-width:90%; height:auto;\" >; We want two factors with a sum of 140, and a product of 4884. I played around with the prime factors and got -2*3*11=-66 and -2*37=-74. So,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-74=0 ALIGN=MIDDLE  ALT=\"y-74=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > OR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-66=0 ALIGN=MIDDLE  ALT=\"y-66=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=74 ALIGN=MIDDLE  ALT=\"y=74\"   DISABLED_style= \"max-width:90%; height:auto;\" > OR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=66 ALIGN=MIDDLE  ALT=\"y=66\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Therefore, the two points are (5,66) and (5,74).<BR>\n" );
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document.write( "Check your work for accuracy.<BR>\n" );
document.write( "Distance between (2,70) and (5,66).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=sqrt%28%285-2%29%5E2%2B%2866-70%29%5E2%29 ALIGN=MIDDLE  ALT=\"D=sqrt%28%285-2%29%5E2%2B%2866-70%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=sqrt%28%283%29%5E2%2B%28-4%29%5E2%29 ALIGN=MIDDLE  ALT=\"D=sqrt%28%283%29%5E2%2B%28-4%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=sqrt%289%2B16%29 ALIGN=MIDDLE  ALT=\"D=sqrt%289%2B16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=sqrt%2825%29 ALIGN=MIDDLE  ALT=\"D=sqrt%2825%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=5 ALIGN=MIDDLE  ALT=\"D=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".\r<BR>\n" );
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document.write( "Distance between(2,70) and (5,74).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=sqrt%28%285-2%29%5E2%2B%2874-70%29%5E2%29 ALIGN=MIDDLE  ALT=\"D=sqrt%28%285-2%29%5E2%2B%2874-70%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=sqrt%28%283%29%5E2%2B%284%29%5E2%29 ALIGN=MIDDLE  ALT=\"D=sqrt%28%283%29%5E2%2B%284%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=sqrt%289%2B16%29 ALIGN=MIDDLE  ALT=\"D=sqrt%289%2B16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=sqrt%2825%29 ALIGN=MIDDLE  ALT=\"D=sqrt%2825%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=5 ALIGN=MIDDLE  ALT=\"D=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "That's it! Feel free to email via gmail if you have questions about the solution<BR>\n" );
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document.write( "Ms.Figgy<BR>\n" );
document.write( "math.in.the.vortex@gmail.com </SPAN>\n" );
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