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In geometry is it true that through any three points exists exactly one line?
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 !?!
How many distinct lines can drawn through two fixed points?
Through any two fixed points, exactly one distinct line can be drawn. This is a fundamental principle in geometry, as two points uniquely determine a straight line. No other line can pass through both points, ensuring the uniqueness of the line connecting them.
Given any three points is there exactly one plane containing them?
Through any three points NOT on the same straight line. If they are all on the same line then that line can act as an axis of rotation for an infinite number of planes containing the three points.
What kind of points determine a plane?
Any three points which do not form a line.
Noncollinear points lie on the same line?
You have to have three or more points to have non-colinear points because any two points determine a line. Noncolinear are NOT on the same line.
Is three distinct points always determine a line?
No, because Of any three points on a line there exists no more than one that lies between the other two.
How many points determine exactly one line?
It takes exactly 2 distinct points to uniquely define a line, i.e. for any two distinct points, there is a unique line containing them.
You can choose any two distinct points on a line to calculate the slope?
A.True
Through any two distinct points there are exists exactly one line?
Yes
Through any two distinct points there exists exactly one line?
False!
Prove the existence of triangles?
1. Given any line, there are at least two points on the line. Call them A and B. 2. Given any line, there exists at least one point in the plane that is not on the line. Call that point C. 3. Given any two points (A and C and, then B and C) there exists a straight line joining them. The point C is not on AB so AB and AC are distinct. Similarly, AB and BC are distinct so that there are three lines that meet, in pairs, at three vertices - and that is a triangle.
In geometry is it true that through any three points exists exactly one line?
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 !?!
Given any three points is there exactly one plane containing them?
Through any three points NOT on the same straight line. If they are all on the same line then that line can act as an axis of rotation for an infinite number of planes containing the three points.
What detemines a unique straight line?
In a Euclidean plane any two distinct points uniquely define a straight line.
What kind of points determine a plane?
Any three points which do not form a line.
Noncollinear points lie on the same line?
You have to have three or more points to have non-colinear points because any two points determine a line. Noncolinear are NOT on the same line.
Three points are collinear true or false?
Not enough information. Collinear means the points are on the same line. If you have any three points, they may, or may not, be on the same line.
