document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=71414>Question 71414</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the distance d(A,B) between the points A(-1,0) and B(4,3).\r<BR>\n" );
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document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #51088 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=51088\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> find the distance d(A,B) between the points A(-1,0) and B(4,3).<BR>\n" );
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document.write( "There is a Distance formula for getting the answer. That formula says:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+sqrt%28%28y2+-+y1%29%5E2+%2B+%28x2+-+x1%29%5E2%29 ALIGN=MIDDLE  ALT=\"D+=+sqrt%28%28y2+-+y1%29%5E2+%2B+%28x2+-+x1%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "In this case you can choose to identify point B as point 2 and point A as point 1. Doing that<BR>\n" );
document.write( "makes y2 =3, x2 = 4, y1 = 0, and x1 = -1.  Now all you have to do is to plug these values<BR>\n" );
document.write( "into the equation and solve as follows:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+sqrt%28%283+-+0%29%5E2+%2B+%284+-+%28-1%29%29%5E2%29+=+sqrt%283%5E2%2B5%5E2%29+=+sqrt%2834%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The answer is that the distance between the points is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2834%29 ALIGN=MIDDLE  ALT=\"sqrt%2834%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "You don't have to memorize the formula, if you think about it.  It is just the Pythagorean<BR>\n" );
document.write( "theorem for a right triangle.  One leg of the triangle is the horizontal or x distance<BR>\n" );
document.write( "between the points and the other leg is the vertical or y distance between the points.<BR>\n" );
document.write( "The hypotenuse then becomes the distance between the points which is what you are looking<BR>\n" );
document.write( "for.  Put a couple of points on a graph. Then call one of the points point 1 and the other <BR>\n" );
document.write( "point 2.  Draw a horizontal line through one of the points and draw a vertical line through<BR>\n" );
document.write( "the other point.  Finally, draw a line connecting the two points.  Notice how a right<BR>\n" );
document.write( "triangle is formed.  Use the Pythagorean theorem to find the distance between the points<BR>\n" );
document.write( "which as you will see is the hypotenuse of the right triangle you have formed. Recall that<BR>\n" );
document.write( "the Pythagorean theorem says:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E2+%2B+B%5E2+=+C%5E2 ALIGN=MIDDLE  ALT=\"A%5E2+%2B+B%5E2+=+C%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "where A is one leg of the right triangle, B is the other leg, and C is the hypotenuse.<BR>\n" );
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document.write( "This, to me, is the easy way to look at this problem, but you certainly can memorize<BR>\n" );
document.write( "the distance formula if you find that easier.<BR>\n" );
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document.write( "Hope this helps with how to understand and solve this problem.<BR>\n" );
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