document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1118057>Question 1118057</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Points J (3, 1) and K (– 1, – 3) are two vertices of an isosceles triangle. If L is the third vertex and has a y-coordinate of 6, what is the x-coordinate of L? </SPAN>\n" );
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document.write( "A sketch shows that, with the two given vertices, the third vertex L of an isosceles triangle with y coordinate 6 will be in quadrant II:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-7%2C5%2C-4%2C8%2C%0D%0Aline%28-5%2C0%2C4%2C0%29%2Cline%280%2C-4%2C0%2C7%29%2Cline%28-1%2C-3%2C3%2C1%29%2Cline%28-7%2C6%2C5%2C6%29%2C%0D%0Alocate%28-2%2C-3.5%2C%22K%28-1-3%29%22%29%2C+locate%283.5%2C1%2C%22J%283%2C1%29%22%29%2C+locate%28-6%2C7%2C%22L%28%3F%2C6%29%22%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "In an isosceles triangle, the altitude to the base is perpendicular to the base at the midpoint of the base.<br><BR>\n" );
document.write( "The midpoint of the base JK is M(1,-1); the slope of the base is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-%28-3%29%29%2F%283-%28-1%29%29=4%2F4=1 ALIGN=MIDDLE  ALT=\"%281-%28-3%29%29%2F%283-%28-1%29%29=4%2F4=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "Then, since the altitude LM is perpendicular to the base JK, the slope of the altitude LM is -1.<br><BR>\n" );
document.write( "Then the equation of the altitude LM to the base JK, using the known point (1,-1), is y = -x.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-7%2C5%2C-4%2C8%2C%0D%0Aline%28-5%2C0%2C4%2C0%29%2Cline%280%2C-4%2C0%2C7%29%2Cline%28-1%2C-3%2C3%2C1%29%2Cline%28-7%2C6%2C5%2C6%29%2C%0D%0Alocate%28-2%2C-3.5%2C%22K%28-1-3%29%22%29%2C+locate%283.5%2C1%2C%22J%283%2C1%29%22%29%2C+locate%28-6%2C7%2C%22L%28%3F%2C6%29%22%29%2C+locate%281%2C-1%2C%22M%281%2C-1%29%22%29%2Cgreen%28line%281%2C-1%2C-7%2C7%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The third vertex L is the point on the altitude where y=6; the equation of the altitude tells us the x value of that point is -6.<br><BR>\n" );
document.write( "So the third vertex L is (-6,6).<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-7%2C5%2C-4%2C8%2C%0D%0Aline%28-5%2C0%2C4%2C0%29%2Cline%280%2C-4%2C0%2C7%29%2Cline%28-1%2C-3%2C3%2C1%29%2Cline%28-7%2C6%2C5%2C6%29%2C%0D%0Alocate%28-2%2C-3.5%2C%22K%28-1-3%29%22%29%2C+locate%283.5%2C1%2C%22J%283%2C1%29%22%29%2C+locate%28-6%2C7%2C%22L%286%2C6%29%22%29%2C+locate%281%2C-1%2C%22M%281%2C-1%29%22%29%2Cgreen%28line%281%2C-1%2C-7%2C7%29%29%2C%0D%0Aline%28-6%2C6%2C-1%2C-3%29%2C+line%28-6%2C6%2C3%2C1%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br> </SPAN>\n" );
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