document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=985338>Question 985338</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Three points have coordinates A(2,5),B(10,9) and C(6,2) ,line two passes through C and is perpendicular to line one.find coordinates of the point of intersection of line one and line two </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #606142 by </B><A HREF=/tutors/aboutme.mpl?userid=Cromlix><B>Cromlix(4381)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Cromlix><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=Cromlix><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=606142\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi there,<BR>\n" );
document.write( "I take it that line 1 is AB.<BR>\n" );
document.write( "gradient of AB = y2-y1/x2-x1<BR>\n" );
document.write( "= 9-5/10-2 = 4/8 = 1/2<BR>\n" );
document.write( "Using the line equation for AB<BR>\n" );
document.write( "Using m = 1/2 and point A (2,5)<BR>\n" );
document.write( "y - 5 = 1/2(x - 2)<BR>\n" );
document.write( "y = 1/2x - 1 + 5<BR>\n" );
document.write( "y = 1/2x + 4<BR>\n" );
document.write( "This is the equation for line AB<BR>\n" );
document.write( "Line C has a gradient of -2<BR>\n" );
document.write( "Lines that are perpendicular have <BR>\n" );
document.write( "gradients that multiply together to give -1<BR>\n" );
document.write( "m1 x m2 = -1<BR>\n" );
document.write( "1/2 x m2 = -1<BR>\n" );
document.write( "m2 = -2<BR>\n" );
document.write( "...........<BR>\n" );
document.write( "Using the line equation:<BR>\n" );
document.write( "y - b = m(x - a)<BR>\n" );
document.write( "Using m = -2 and pt C (6,2)<BR>\n" );
document.write( "y - 2 = -2(x - 6)<BR>\n" );
document.write( "y = -2x + 12 + 2<BR>\n" );
document.write( "y = -2x + 14<BR>\n" );
document.write( "This the equation of line C<BR>\n" );
document.write( "Setting up simultaneous equations:<BR>\n" );
document.write( "y - 1/2x = 4 ....(1)<BR>\n" );
document.write( "y + 2x = 14 .....(2)<BR>\n" );
document.write( "Multiply (1) by 4<BR>\n" );
document.write( "4y - 2x = 16 .....(1)<BR>\n" );
document.write( "y + 2x = 14  .....(2)<BR>\n" );
document.write( "Add (1) + (2)<BR>\n" );
document.write( "5y = 30<BR>\n" );
document.write( "y = 6<BR>\n" );
document.write( "Substitute y = 6 into:<BR>\n" );
document.write( "y + 2x = 14<BR>\n" );
document.write( "6 + 2x = 14<BR>\n" );
document.write( "2x = 14 - 6<BR>\n" );
document.write( "2x = 8<BR>\n" );
document.write( "x = 4<BR>\n" );
document.write( "{4,6} the point of intersection<BR>\n" );
document.write( "of line AB and C<BR>\n" );
document.write( "Hope this helps:-)<BR>\n" );
document.write( " </SPAN>\n" );
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