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If you take the generic equation for a circle, and make three equations out of it by
substituting the coordinates of the three points, you can solve them simultaneously
and derive a single solution for the center and radius of a circle. In other words, you
can always find one, and only one, circle that those three points lie on.
You have to be able to sing and dance pretty well in the key of algebra to do that, but
once you've done it, it feels great. Then your next exercise is to write a simple computer
program that takes the three points as an input, and outputs the center and radius of
the circle. We wrote that once, when we wanted a tool to explore the outline of the
Mandelbrot set. Totally useless, and loads of fun.
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How many planes can be drawn through any three noncollinear points in a plane?
just one
Are three noncollinear points always contained in only one plane?
Yes a plane can always be drawn three any three points, whether they are linear or not.
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.
Can two points be noncollinear?
No. Any two points can be made to form a line.
Can noncollinear parts lie on the same plane?
Yes. In fact any three points that are not collinear define a plane and therefore MUST lie on a plane.
What is there through any three noncollinear points?
A plane. A circle can also pass through three non-co-linear points.
Can noncollinear points lie on a circle?
Yes. In fact, given any three non-collinear points, there is one (and only one) circle that passes through all three points.
How many planes can be drawn through any three noncollinear points in a plane?
just one
Are three noncollinear points always contained in only one plane?
Yes a plane can always be drawn three any three points, whether they are linear or not.
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.
How many points does a noncollinear plane has?
Any Euclidean plane has infinitely many points.
Can two points be noncollinear?
No. Any two points can be made to form a line.
How many planes can be drawn through any three noncollinear points?
Only one plane can pass through 3 non-collinear points.
From any point on a property a surveyor can locate a straight line to any other point on the property?
Through any three noncollinear points, there is exactly one plane.
Can you draw a figure with three points that are noncollinear?
Of course. The vertices of a triangle, and any three vertices of any other polygon, are non-collinear. In the case of a triangle and a quadrilateral, if you had three collinear vertices, then you couldn't have the polygon.
Can noncollinear parts lie on the same plane?
Yes. In fact any three points that are not collinear define a plane and therefore MUST lie on a plane.
Can three points be noncoplanar?
No, A plane can be drawn through any 3 points. If the 3 points are collinear then they make a line and a plane can contain a line. If the points are noncollinear then they can be used to form the corners of a triangle; all points of a triangle are in the same plane.
