document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=764907>Question 764907</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The coordinates of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B ALIGN=MIDDLE  ALT=\"B\"   DISABLED_style= \"max-width:90%; height:auto;\" > are (2,-4) and (0,3) respectively. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a point on the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L ALIGN=MIDDLE  ALT=\"L\"   DISABLED_style= \"max-width:90%; height:auto;\" > such that the area of the triangle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ABC ALIGN=MIDDLE  ALT=\"ABC\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8+unit%5E2 ALIGN=MIDDLE  ALT=\"8+unit%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Find the two possible equation of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L ALIGN=MIDDLE  ALT=\"L\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #465877 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=465877\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Line AB is y=-(7/2)x+3, and the line perpendicular to it at point (0,3) is y=(2/7)x+3.  The point (0,3) here was picked arbitrarily for convenience.  \r<BR>\n" );
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document.write( "Using segment AB as a base of the triangle, distance formula, steps here omitted,... the base AB is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2853%29 ALIGN=MIDDLE  ALT=\"sqrt%2853%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  \r<BR>\n" );
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document.write( "Triangle with 8 unit^2 will have an altitude value h, so that:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%28sqrt%2853%29%29%2Ah=8 ALIGN=MIDDLE  ALT=\"%281%2F2%29%28sqrt%2853%29%29%2Ah=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28h=16%2Fsqrt%2853%29%29 ALIGN=MIDDLE  ALT=\"highlight%28h=16%2Fsqrt%2853%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "What point is h units away from (0,3) and is on line y=(2/7)x+3?<BR>\n" );
document.write( "That refers to another distance and the use of distance formula again.<BR>\n" );
document.write( "We want those two,  variable points of (x, (2/7)x+3).<BR>\n" );
document.write( "Applying distance formula,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=16%2Fsqrt%2853%29=sqrt%28%28x-0%29%5E2%2B%28%282%2F7%29x%2B3-3%29%5E2%29 ALIGN=MIDDLE  ALT=\"h=16%2Fsqrt%2853%29=sqrt%28%28x-0%29%5E2%2B%28%282%2F7%29x%2B3-3%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which will simplify to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=-112%2F53%29 ALIGN=MIDDLE  ALT=\"highlight%28x=-112%2F53%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=112%2F53%29 ALIGN=MIDDLE  ALT=\"highlight%28x=112%2F53%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From those two values, you can use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%282%2F7%29x%2B3 ALIGN=MIDDLE  ALT=\"y=%282%2F7%29x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to determine the corresponding values for y.\r<BR>\n" );
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document.write( "Can you finish the rest of the way to the needed line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%287%2F2%29x%2Bg ALIGN=MIDDLE  ALT=\"y=-%287%2F2%29x%2Bg\"   DISABLED_style= \"max-width:90%; height:auto;\" > for some y-intercept g ?\r<BR>\n" );
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document.write( "Just to show final answer without the remaining steps,<BR>\n" );
document.write( "lines wanted are:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=-%287%2F2%29x%2B519%2F53%29 ALIGN=MIDDLE  ALT=\"highlight%28y=-%287%2F2%29x%2B519%2F53%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=-%287%2F2%29x%2B11%29 ALIGN=MIDDLE  ALT=\"highlight%28y=-%287%2F2%29x%2B11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and know that point C is really still a variable point. </SPAN>\n" );
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