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Would a single point and a fixed distance determine a unique segment in 2-space or 3-space like it does in 1-space when given the length of the segment and location of its midpoint? Please explain your answer.

I think it would be a unique segment in both 2-space and 3-space. But I have no back up. How can I use GeoGebra to show this?

Donna
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  • In $2$-dimensional space, the segment might be horizontal, or vertical, or pointing in some other direction. – Angina Seng Sep 04 '18 at 02:58
  • When you define a segment you get a line. When you define the half segment (point and mid-point) you get the same line. With GeoGebra draw a sphere with the midpoint as center and intersect the line with the sphere. – Moti Sep 04 '18 at 04:00
  • I see what you are saying but how do I explain it? – Donna Sep 04 '18 at 20:40

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