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What is the locus of all points in the plane 3 cm from a given segment?
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∙ 12y ago
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Does a plane containing 2 points of a line contains the entire line?
Yes, a plane containing 2 points of a line contains the entire line. Let us consider two points on a plane and then draw a line segment joining those two points. Since the points lie on the plane so line segment has to lie completely on that plane too. Now if we extend the line segment indefinitely in both directions we get a line and that line also has to lie on the same plane since some definite part(line segment) of it(line) also lies on the same plane.
Can a plane bisect a segment?
No
What is the intersection of plane WZVS and plane STUV?
Points S and V
If three points are coplanar then are they collinear?
Not necessarily. Coplanar means that points lie on the same plane whereas collinear means that points lie on the same line. Points on a plane do not necessarily lie along the same line.
Any three points must be?
... in the same plane.
Locus of all points in a plane equidistant from a given point?
A Circle.
What is the locus of points in a plane that are equidistant from points A and B in the plane?
a straight line ..
What is the locus of points at a given distance of a line?
The locus of points at a given distance to a line would be a line parallel to the first line. Assuming that both lines are straight.
What figure is the locus of all points that are equidistant from two fixed points?
A line in 2D and a plane in 3D A perpendicular bisector of the line connecting the 2 given points
What is the locus of points in space that are equidistant from two parallel planes?
A plane midway between the two given planes and parallel to them.
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.
What is the locus of points in a plane that are equidistant from two fixed points?
I believe that is the definition of a straight line.
What is the locus of points in a plane equidistant from the sides of an angle?
A line that is the angle bisector.
How is the locus of points equidistant from two parallel lines in a plane constructed?
you dont
What is connecting two points on a plane?
A line segment would connect two points on a plane.
Although the locus of points idea can be used to define a straight line and circle more complex shapes such as parabolas must be defined a different way. True or False?
Certainly false for parabolae; a parabola is the locus of points in a plane which are equidistant from a point (the focus) and a line (the directrix) in that plane. It's also false for an ellipse, which is the locus of points in a plane where the sum of the distances from two other points in that plane (the foci) is constant. AND false for a hyperbola, which is the locus of points in a plane where the absolute value of the DIFFERENCE in the distance from two points in that plane (also the foci) is constant. Alternatively, a hyperbola is the locus of points in a plane where the ratio of the distance to one of the foci and to a line (the directrix) is constant (which is larger than 1; if it's exactly equal to 1, you get a parabola instead).All of these are only slightly more complicated than circles, and in fact they, alone with circles, are called "conic sections" because they all are formed by the intersection of a plane with a right circular conical surface.
Does a plane containing 2 points of a line contains the entire line?
Yes, a plane containing 2 points of a line contains the entire line. Let us consider two points on a plane and then draw a line segment joining those two points. Since the points lie on the plane so line segment has to lie completely on that plane too. Now if we extend the line segment indefinitely in both directions we get a line and that line also has to lie on the same plane since some definite part(line segment) of it(line) also lies on the same plane.
