document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203459>Question 1203459</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Triangle $ABC$ has vertices $A(2, 3),$ $B(1, -8)$ and $C(-3, 2).$ The line containing the altitude through $A$ intersects the point $(0, y).$ What is the value 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 #839035 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=839035\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answer:   <font color=red>y = 11/5 = 2.2</font>\r<BR>\n" );
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document.write( "Explanation\r<BR>\n" );
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document.write( "Compute the slope of line BC<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+slope+=+rise%2Frun+=+matrix%281%2C3%2C%22change%22%2C%22in%22%2C%22y%22%29%2Fmatrix%281%2C3%2C%22change%22%2C%22in%22%2C%22x%22%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%282+-+%28-8%29%29%2F%28-3+-+1%29 ALIGN=MIDDLE  ALT=\"m+=+%282+-+%28-8%29%29%2F%28-3+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%282+%2B+8%29%2F%28-3+-+1%29 ALIGN=MIDDLE  ALT=\"m+=+%282+%2B+8%29%2F%28-3+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%2810%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"m+=+%2810%29%2F%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+-5%2F2 ALIGN=MIDDLE  ALT=\"m+=+-5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The slope of -5/2 means \"go down 5 units every time we go 2 units to the right\".<BR>\n" );
document.write( "In short: \"down 5, right 2\".\r<BR>\n" );
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document.write( "The negative reciprocal slope will have us do two things:<BR>\n" );
document.write( "flip the fraction<BR>\n" );
document.write( "flip the sign\r<BR>\n" );
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document.write( "-5/2 becomes 2/5\r<BR>\n" );
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document.write( "The altitude line through point A has a slope of 2/5<BR>\n" );
document.write( "Apply point-slope form<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+-+y%5B1%5D+=+m%28x+-+x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"y+-+y%5B1%5D+=+m%28x+-+x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+-+y%5B1%5D+=+%282%2F5%29%28x+-+x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"y+-+y%5B1%5D+=+%282%2F5%29%28x+-+x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in perpendicular slope\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+-+3+=+%282%2F5%29%28x+-+2%29 ALIGN=MIDDLE  ALT=\"y+-+3+=+%282%2F5%29%28x+-+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in coordinates of point A\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+-+3+=+%282%2F5%29x+%2B+%282%2F5%29%28-2%29 ALIGN=MIDDLE  ALT=\"y+-+3+=+%282%2F5%29x+%2B+%282%2F5%29%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+-+3+=+%282%2F5%29x+-+4%2F5 ALIGN=MIDDLE  ALT=\"y+-+3+=+%282%2F5%29x+-+4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%282%2F5%29x+-+4%2F5+%2B+3 ALIGN=MIDDLE  ALT=\"y+=+%282%2F5%29x+-+4%2F5+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%282%2F5%29x+-+4%2F5+%2B+3%2A%285%2F5%29 ALIGN=MIDDLE  ALT=\"y+=+%282%2F5%29x+-+4%2F5+%2B+3%2A%285%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%282%2F5%29x+-+4%2F5+%2B+15%2F5 ALIGN=MIDDLE  ALT=\"y+=+%282%2F5%29x+-+4%2F5+%2B+15%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%282%2F5%29x+%2B+%28-4+%2B+15%29%2F5 ALIGN=MIDDLE  ALT=\"y+=+%282%2F5%29x+%2B+%28-4+%2B+15%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%282%2F5%29x+%2B+11%2F5 ALIGN=MIDDLE  ALT=\"y+=+%282%2F5%29x+%2B+11%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is the equation of the altitude through point A. It is perpendicular to side BC.\r<BR>\n" );
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document.write( "Plug in x = 0 to find that y = 11/5 = 2.2 which is the final answer.\r<BR>\n" );
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document.write( "Here's the diagram<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28500%2C500%2C-10%2C10%2C-10%2C10%2C%0D%0Agraph%28500%2C500%2C-10%2C10%2C-10%2C10%2C-1000%29%2C%0D%0A%0D%0Acircle%282%2C3%2C0.1%29%2Ccircle%282%2C3%2C0.12%29%2Ccircle%282%2C3%2C0.14%29%2Ccircle%282%2C3%2C0.16%29%2Ccircle%281%2C-8%2C0.1%29%2Ccircle%281%2C-8%2C0.12%29%2Ccircle%281%2C-8%2C0.14%29%2Ccircle%281%2C-8%2C0.16%29%2Ccircle%28-3%2C2%2C0.1%29%2Ccircle%28-3%2C2%2C0.12%29%2Ccircle%28-3%2C2%2C0.14%29%2Ccircle%28-3%2C2%2C0.16%29%2Ccircle%280%2C2.2%2C0.1%29%2Ccircle%280%2C2.2%2C0.12%29%2Ccircle%280%2C2.2%2C0.14%29%2Ccircle%280%2C2.2%2C0.16%29%2C%0D%0A%0D%0Alocate%282.3%2C2.7%2C%22A%22%29%2Clocate%281.3%2C-8.3%2C%22B%22%29%2Clocate%28-2.7-1%2C1.7%2B1%2C%22C%22%29%2Clocate%280.3%2C1.9%2C%22D%22%29%2C%0D%0A%0D%0Aline%282%2C3%2C1%2C-8%29%2Cline%281%2C-8%2C-3%2C2%29%2Cline%28-3%2C2%2C2%2C3%29%2C%0D%0A%0D%0Aline%28-2.21034%2C1.31586%2C-2.03241%2C0.87103%29%2Cline%28-2.03241%2C0.87103%2C-2.47724%2C0.6931%29%2C%0D%0A%0D%0Ablue%28line%282%2C3%2C-2.65517%2C1.13793%29%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The blue line is the altitude through point A. <BR>\n" );
document.write( "It intersects the y axis at (0, 11/5) = (0,2.2) which is marked as point D.<BR>\n" );
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