document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=297859>Question 297859</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello,\r<BR>\n" );
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document.write( "I have 4 points given to me and I have to prove algebraically whether the figure is a kite.  I can't just plot the points.  How would I go about doing that? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #214423 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=214423\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given 4 points, divide them into two sets. <BR>\n" );
document.write( "One set is the lengthwise component on the kite (line AB below). <BR>\n" );
document.write( "The other set is the transverse (sideways) component of the kite (line CD).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-2%2C10%2C-2%2C10%2C%0D%0Alocate%281.5%2C6.25%2CC%29%2C%0D%0Alocate%286.25%2C2%2CD%29%2C%0D%0Alocate%280.25%2C0%2CA%29%2C%0D%0Alocate%286.25%2C6%2CB%29%2C%0D%0Alocate%284.5%2C4.2%2CI%29%2C%0D%0Ablue%28line%280%2C0%2C6%2C6%29%29%2Cgreen%28line%282%2C6%2C6%2C2%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Calculate the eqaution of the line using the slope and the point-slope form of a line for the length wise component.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-ya=m1%28x-xa%29 ALIGN=MIDDLE  ALT=\"y-ya=m1%28x-xa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m1=%28yb-ya%29%2F%28xb-xa%29 ALIGN=MIDDLE  ALT=\"m1=%28yb-ya%29%2F%28xb-xa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then convert to slope-intercept form<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=m1%2Ax%2Bb1 ALIGN=MIDDLE  ALT=\"y=m1%2Ax%2Bb1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Do the same for the transverse component to get its equation,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=m2%2Ax%2Bb2 ALIGN=MIDDLE  ALT=\"y=m2%2Ax%2Bb2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If it's a kite, the lines will be perpendicular and the relationship between the two slopes will be,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m1%2Am2=-1 ALIGN=MIDDLE  ALT=\"m1%2Am2=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If that's not the case, then stop there. It's not a kite.<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
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document.write( "If it is true then find the intersection point, I, between the two lines. <BR>\n" );
document.write( "Solve the system of equations.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=m1%2Ax%2Bb1 ALIGN=MIDDLE  ALT=\"y=m1%2Ax%2Bb1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=m2%2Ax%2Bb2 ALIGN=MIDDLE  ALT=\"y=m2%2Ax%2Bb2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since they both equal y, set them equal to each other.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m1%2Axi%2Bb1=m1%2Axi%2Bb2 ALIGN=MIDDLE  ALT=\"m1%2Axi%2Bb1=m1%2Axi%2Bb2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solve for x.<BR>\n" );
document.write( "Then solve for y using either equation. <BR>\n" );
document.write( "Now you have the point of intersection (xi,yi) of the two components of the kite.<BR>\n" );
document.write( "If it's a kite, the distance from the intersection point (xi,yi) to the ends of the transverse components (C and D) must be identical. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Dci=Ddi ALIGN=MIDDLE  ALT=\"Dci=Ddi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Dci%5E2=Ddi%5E2 ALIGN=MIDDLE  ALT=\"Dci%5E2=Ddi%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28xc-xi%29%5E2%2B%28yc-yi%29%5E2=%28xd-xi%29%5E2%2B%28yd-yi%29%5E2 ALIGN=MIDDLE  ALT=\"%28xc-xi%29%5E2%2B%28yc-yi%29%5E2=%28xd-xi%29%5E2%2B%28yd-yi%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If that's the case, then you've proven that the points form a kite. <BR>\n" );
document.write( "If it's not true, then you don't have a kite. <BR>\n" );
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