document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=176789>Question 176789</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the point that is one-fourth of the distance from the point P(-1,3) to the point Q(7,5) along the segment PQ </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #131888 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=131888\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the point that is one-fourth of the distance from the point P(-1,3) to the point Q(7,5) along the segment PQ<BR>\n" );
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document.write( "Plot the points.<BR>\n" );
document.write( "Let PQ be the hypotenuse of a rt. triangle with 3rd point R(7,3)<BR>\n" );
document.write( "Find length of PQ: sqrt(8^2+2^2) = sqrt(68) = 2sqrt(17)<BR>\n" );
document.write( "(1/4)2sqrt(17) = (1/2)sqrt(17)<BR>\n" );
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document.write( "let a point (1/4)th of the way from P to Q be M(x,y)<BR>\n" );
document.write( "Draw a line segment from M perpendicular to PR at N.<BR>\n" );
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document.write( "Triangle PMN is proportional to Triangle PQR.<BR>\n" );
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document.write( "A point (1/4) of the way from P to R is (1,3)<BR>\n" );
document.write( "A point (1/4) of the way from R to Q is (7,3 1/2)<BR>\n" );
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document.write( "so the point (1/4) of the way from P to Q is (1,(7/2))<BR>\n" );
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document.write( "Prove it:<BR>\n" );
document.write( "distance from P to Q = sqrt[(1--1)^2 + (3-(7/2)^2] = sqrt[4 + 1/4] <BR>\n" );
document.write( "= sqrt[17/4] = (1/2)sqrt(17)<BR>\n" );
document.write( "and this is (1/4) the way from P to Q.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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