Midpoint Formula and Trisection Points
Date: 09/05/2003 at 00:40:29 From: Sarah Subject: The Cartesian Plane and the Distance Formula Show that ((1/3)(2x_1+ x_2), (1/3)(2y_1+y_2)) is one of the points of trisection of the line segment joining (x_1,y_1) and (x_2,y_2). It seems to me that the answer should be related to the midpoint formula, but I just can't figure it out.
Date: 09/05/2003 at 12:52:42 From: Doctor Peterson Subject: Re: The Cartesian Plane and the Distance Formula Hi, Sarah. You're right, it is related to the mispoint formula; if you understand where that comes from, you should be able to derive this formula. So they are testing your deeper understanding of the idea of the midpoint. Here is our segment: (x_2,y_2) o /| / | / | / | / | o-----+ /| | / | | / | | / | | / | | o-----+-----+ /| | | / | | | / | | | / | | | / | | | o-----+-----+-----+ (x_1,y_1) Note that when we divide the segment into three equal parts, we are also dividing the horizontal and vertical legs of this right triangle into three equal parts. (Think similar triangles!) Now, in terms of the coordinates, how long is that horizontal segment? How long is each third? How much do we have to add to x_1 to find the x-coordinate of each intermediate point? What are those coordinates? I think that should lead you through the work. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
Date: 09/09/2003 at 23:14:19 From: Sarah Subject: Thank you Thank you very much! It was much simpler than I thought.
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.