document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=230539>Question 230539</A>: <I><SPAN STYLE=\"word-break: break-all;\"> plz help me to solve this question.....\r<BR>\n" );
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document.write( "Q.  Three points have coordintes A(4,13), B(9,3) and  C(10,8).Find the equation of<BR>\n" );
document.write( "(a) the line AB<BR>\n" );
document.write( "(b) the line through C perpendicular to the line y-4x=5.<BR>\n" );
document.write( "     the line through C meets the line AB at point P.Calculate the coordinates of P<BR>\n" );
document.write( "     and the ratio AP:PB<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #170729 by </B><A HREF=/tutors/aboutme.mpl?userid=algebrapro18><B>algebrapro18(249)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=algebrapro18><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=170729\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In order to do this we will need to remember a few key facts:<br>\r<BR>\n" );
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document.write( "1) the equation to find the slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28y2-y1%29%2F%28x2-x1%29 ALIGN=MIDDLE  ALT=\"m+=+%28y2-y1%29%2F%28x2-x1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2) the point slope formula for a line is y-y1=m(x-x1)<BR>\n" );
document.write( "3) Perpendicular lines have opposite reciprical slopes<BR>\n" );
document.write( "4) the slope intercept form of a line is y=mx+b<br>\r<BR>\n" );
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document.write( "Now on to solving your problem.  <br>\r<BR>\n" );
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document.write( "Part A: Find the equation of the line AB.<BR>\n" );
document.write( "Well we know point A and point B so we can find the slope by using equation 1.<br>\r<BR>\n" );
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document.write( "m = (3-13)/(9-4) = -2<br>\r<BR>\n" );
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document.write( "Now that we have the slope of the line and a point on the line we can use equation 2 to find the equation of the line.<br>\r<BR>\n" );
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document.write( "y-y1=m(x-x1)<BR>\n" );
document.write( "y-3=-2(x-9)<br>\r<BR>\n" );
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document.write( "I will leave the simplification to you but you should end up with the equation being y=-2x+21.<br>\r<BR>\n" );
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document.write( "Part B Subpart 1:  Find the equation of  the line through C perpendicular to line y-4x=5.<br>\r<BR>\n" );
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document.write( "To do this we need to get the equation of the given line into slope-intercept form and then we can use fact 3 to find the slope of the line we are finding.  To get the line into slope intercept form all we have to do is add 4x to both sides.<br>\r<BR>\n" );
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document.write( "y = 4x+5<br>\r<BR>\n" );
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document.write( "So we know this line has a slope of 4 so the line we are finding the equation of will have a slope of -1/4 by fact 3.  Now that we have a point on the line and its slope we can use equation 2 again and find the equation of the line we are looking for.  I will leave the algebra to you but you should get y=-1/4x+21/2 for your equation.  <br>\r<BR>\n" );
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document.write( "Part B Subpart 2:  Find the point where the two lines we found intersect.  <br>\r<BR>\n" );
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document.write( "To do this we solve the system of equations.<br>\r<BR>\n" );
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document.write( "y = -2x + 21<BR>\n" );
document.write( "y = -1/4x + 21/2<br>\r<BR>\n" );
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document.write( "Since both are equal to y we can set both equations equal and solve for x.  I will leave the algebra for you to do but you should get that x = 6.  NOw that we know x = 6 we can substitute that back into either equation.  Again I will leave this for you to do but you should get y = 9.  So point P is (6,9).<br>\r<BR>\n" );
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document.write( "Now I'm not sure how to do the rest of this problem so I'm sorry.  Let me know if you need more assistance.   </SPAN>\n" );
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