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A series of 3 points will always determine a plane unless 2 or all 3 points are identical points (they have the same coordinates).

If the idea is to have the three points determine oneplane, a unique plane, then three points will do that as long as none of them have the same spacial coordinates (have identical locations) or as long as the three points do not lie on a single line.

If a straight line can be drawn through all three points, they will not form one unique plane either.

Q: When would three points not determine a plane?

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I would say that there are an infinite number of planes that can pass through a pair of skew lines. In order to find the equation of a plane, all you need is three points. take two points off of one line and one point off of the other line and you should be able to derive the equation of a plane. Since the number of points on a line is infinite, an infinite number of planes can be derived.

To place four points equidistant from each other, you would need to arrange them in the shape of a perfect square. This means that each point would be the same distance away from the other three points, forming equal sides of the square. The distance between each point can be calculated using the Pythagorean theorem if the coordinates of the points are known.

I'm not sure, but I would imagine they would be 360O around the point and only in the same plane.

A plane is a flat, closed figure.a flat surface on which a straight line joining any two points on it would wholly lie:

A circle or a sphere would fit the given description.

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If you were to have 3 points on the same line, then you would actually not be determining a plane, because there are infinitely many planes that can intersect a given line. But if you have 3 points in the form of the points (or vertices) of a triangle, then you determine a plane in the sense that there is only one possible plane upon which that triangle can be drawn (not including a degenerate triangle, which is equivalent to a line).

Any 3 geometric points, as long as they are all in different locations and not superimposed on each other, will define a plane. In other words, there is only one plane that can pass through 3 distinct points. If you had only two points, it would define a line, but not a plane. A plane can include 2 points but if there are only 2 that are specified, the plane can rotate around those 2 points, generating infinitely many planes.

yes, three points in the least number of points that can be used to define a plane. if you used two points you would only have a line, and one point is a point

Three collinear points don't define a plane."Define" means narrow it down to one and only one unique plane, so that it can't be confused with any other one.There are many different planes (actually infinite) that can contain three collinear points, so no unique plane is defined.

A line segment would connect two points on a plane.

In geometry, a plane is a flat two-dimensional "surface" (similar to a sheet of paper, but with no thickness and no finite length or width). A plane is defined by three points, each of which forms a line with the other two points within the plane. In three dimensions, the simplest version of a plane would include all of the points with any x and y value that contain the same value for z.A plane is a flat surface or a 2-dimensional object, stretching to infinity in all directions.

No, given any three points, it is possible for one of the points not to be on the line defined by the other two points. Only two points on a line are needed to identify the exact position of the line. The positions of any three points gives you the exact position of the plane that includes those three points.No, it is not true. If it were true, all triangles would be straight lines !?!

I am assuming that you are in a three dimensional world. Then the three planes of projection would be the xy plane, the xz plane, and the yz plane.

putting a dot

Compared to a 3-legged stool it would. Consider the 3 or 4 points where the bottom of the legs make contact with the floor (which need not be even). Any three points are always in one plane so all points of contact for a 3-legged stool will always lie in the plane, thereby preventing rocking. Four points need not be coplanar and if they are not, the stool will rock.

One line only. This is because by definition a line only needs two points. Three points not in a line would make a plane when connected. Two points, when connected, form a line in which there is only one way to pass through points a and b.

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