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Is a segment an infinite set of points?
CIRCLE
What is the set of two fixed points and all points in between them?
It is a line segment.
Why can you not define a line as an infinate set of points?
An infinite set of points can be a microscopically small line segment. An infinite number of points does not mean an infinitely long line.
Given two points A and B in the three dimensional space what is the set of points equidistant from A and B?
A plane is the set of all points in 3-D space equidistant from two points, A and B. If it will help to see it, the set of all points in a plane that are equidistant from points A and B in the plane will be a line. Extend that thinking off the plane and you'll have another plane perpendicular to the original plane, the one with A and B in it. And the question specified that A and B were in 3-D space. Another way to look at is to look at a line segment between A and B. Find the midpoint of that line segment, and then draw a plane perpendicular to the line segment, specifying that that plane also includes the midpoint of the line segment AB. Same thing. The set of all points that make up that plane will be equidistant from A and B. At the risk of running it into the ground, given a line segment AB, if the line segment is bisected by a plane perpendicular to the line segment, it (the plane) will contain the set of all points equidistant from A and B.
is this statement true or falseA perpendicular bisector is the set of points that are equidistant from the endpoints of the bisected segment.?
true
