document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=339327>Question 339327</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the distance of the z-intercept from the x-intercept in the equation ax+by+cz+d=0. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #243238 by </B><A HREF=/tutors/aboutme.mpl?userid=nyc_function><B>nyc_function(2741)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nyc_function><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=nyc_function><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=243238\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The plane crosses the x axis when y = z = 0; similarly x = y = 0 when it crosses the z-axis. We have to make some assumptions about the coefficients a and c---namely that they are not zero so that the plane does actually cross these axes. (Well, there is the other degenerate case in which the plane is the xz-plane y = 0.)\r<BR>\n" );
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document.write( "If a and c are nonzero, the intersection of the plane with the x-axis occurs at the point (-d/a,0,0) and that with the z-axis occurs at (0,0,-d/c). The distance between these points is \r<BR>\n" );
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document.write( "&#8730;((-d/a)^2 + (-d/c)^2) = |d|/&#8730;(a^2 + c^2)<BR>\n" );
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