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Algebra and Trigonometry
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In Mathematics we often say "the set of all points that ... ".
What does it mean?
Points can make a line |
Example: A Circle is:
"the set of all points on a plane that are a fixed distance from a central point".
So, just a few points start to look like a circle, but when we collect ALL the points we will actually have a circle.
Try drawing one yourself (move any point):
images/geom-locus.js
(Note: the points are drawn as dots so you can see them,
but they really should have no size at all)
Surface
Imagine this happening in 3D space: all the points that are a fixed distance from a center make a sphere!
Locus
The idea of "the set of all points that ..." is used so much it has a name: Locus.
A Locus is a set of points that share a property.
So, a circle is "the locus of points on a plane that are a fixed distance from the center".
Note: "Locus" usually means that the points make a continuous curve or surface.
Example: An ellipse is the locus of points whose distance from two fixed points add up to a constant.
So, no matter where we are on the ellipse, we can add up the distance to point "F" and to point "G" and it will always be the same result.
(The points "F" and "G" are called the foci of the ellipse)
The idea of "Locus" can be used to create some weird and wonderful shapes!
7922, 7923, 7924, 7925, 7926, 7927, 7928, 7929, 7930, 7931
The set of all points in a plane that lie the same distance from a single point in the plane.Which one is the answer
(i) Collinear(ii) Angle(iii) Circle(iv) Coplanar
Solution:
The set of all points in a plane that lie the same distance from a single point in the plane is a circle.
Therefore, option (iii) is the correct answer.
From the above figure, we observe that for the different position of the point P, its distance from the fixed point O (centre) is the same.
Collinear: Three or more points that lie on the same line are collinear points .
Angle : In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle.
Coplanar : A set of points in space are coplanar if there exists a geometric plane that contains them all.
Summary:
The set of all points in a plane that lie the same distance from a single point in the plane is a circle.
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What is the definition of a circle?
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What is the definition of a circle?
A circle is the set of all points in a plane that are the same distance from a fixed point called the center.
A circle is a set of all points that are the same distance form a fixed point called the center.
A circle is the set of all points in a plane that are a given distance from a given line.
A circle is the distance from a set of points to a fixed point called the center.
Jazminfun0128182 Feb 28, 2018
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A circle is the set of all points in a plane that are the same distance from a fixed point called the center.
CPhill Feb 28, 2018
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