David Little
Mathematics Department
Penn State University
Eberly College of Science
University Park, PA 16802
Office: 403 McAllister
Phone: (814) 865-3329
Fax: (814) 865-3735
e-mail:dlittle@psu.edu

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Constructing The Midpoint
Our goal is to find the unique point that is equidistant from the red and green points and lies on the line through these points.

To do so, first draw a line segment using the red and green points as endpoints. Next, draw two circles just as we did in Constructing An Equilateral Triangle. The first circle is centered at the red point and passes through the green point. The second circle is centered at the green point and passes through the red point.

Next, find the two points of intersection for the circles you just drew. Now, draw a line through these two points of intersection. And finally, intersection this line with the line segment you drew at the beginning.

This point of intersection is the midpoint of the red and green points. Can you explain why?