document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189872>Question 1189872</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This question is really all about Distance and Midpoint Formula\r<BR>\n" );
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document.write( "You are going on a two-day hike. The map at the right shows the trails you plan to follow. (Each unit represents 1 mile.)\r<BR>\n" );
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document.write( "a. You hike from the lodge to point A and decide that you will hike to the midpoint of AB before you camp for the night. At what point in the plane will you be camping?\r<BR>\n" );
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document.write( "b. How far will you hike each day?\r<BR>\n" );
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document.write( "I think I can’t post the illustration but I hope opening this link would help https://mrrossatgradyhigh.files.wordpress.com/2016/08/10-1-distance-and-midpoint-formulas.pdf<BR>\n" );
document.write( "(Located 4th page of the pdf, question number 16)\r<BR>\n" );
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document.write( "Answering this question would help me a lot, thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821381 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=821381\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the midpoint from point A to point B would be found by the formula:<BR>\n" );
document.write( "midpoint = ((x1 + x2)/2, (y1 + y2)/2)\r<BR>\n" );
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document.write( "(x1,y1) = (-3,2)<BR>\n" );
document.write( "(x2,y2) = (2,6)\r<BR>\n" );
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document.write( "midpoint is equal to ((-3 + 2)/2, (2 + 6)/2) which is equal to (-1/2,4).<BR>\n" );
document.write( "this can also be shown as (-.5,4).\r<BR>\n" );
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document.write( "you will be camping at the point (-1/2, 4).<BR>\n" );
document.write( "we'll call that point C.<BR>\n" );
document.write( "point C is the midpoint between point A and point B.\r<BR>\n" );
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document.write( "on the first day, you will have hiked from the lodge to point A and then to point C.\r<BR>\n" );
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document.write( "the distance between the lodge and point A is equal to sqrt((-3)^2 + 2^2) = sqrt(9 + 4) = sqrt(13).\r<BR>\n" );
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document.write( "point A is at (-3,2).<BR>\n" );
document.write( "point C is at (-.5,4).<BR>\n" );
document.write( "-.5 - (-3) is equal to 2.5<BR>\n" );
document.write( "4 - 2 is equal to 2<BR>\n" );
document.write( "the distance between point A and point C is equal to sqrt(2.5^2 + 2^2) which is equal to sqrt(6.25 + 4) which is equal to sqrt(10.25).\r<BR>\n" );
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document.write( "the distance traveled from the lodge to point A and then to point C is therefore equal to sqrt13) + sqrt(10.25) = 6.807113394 kilometers.\r<BR>\n" );
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document.write( "if you continue in the same direction you were traveling to complete the loop from the lodge to point A to point B to the lodge, then you will be traveling from point C to point B to the lodge on the second day.\r<BR>\n" );
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document.write( "the distance from point C to point B is the same as the distance from point A to point C, which is equal to sqrt(10.25).\r<BR>\n" );
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document.write( "the distance between point B and the lodge is equal to sqrt(2^2 + 6^2) = sqrt(4 + 36) = sqrt(40).\r<BR>\n" );
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document.write( "the total distance you travel on the second day must be sqrt(10.25) + sqrt(40) = 9.526117439 kilometers.\r<BR>\n" );
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document.write( "your solution is that you stopped at the point (-.5,4) at the end of the first day and that you traveled 6.807113394 kilometers on the first day and 9.526117439 kilometers on the second day.\r<BR>\n" );
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document.write( "let me know if you have any questions.\r<BR>\n" );
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document.write( "theo\r<BR>\n" );
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document.write( " </SPAN>\n" );
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