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What is a shape consisting of all the points a given distance from a center point?
A circle.
A compass draws all points that are equidistant from a fixed point thereby creating a locus of points for a circle?
A circle is the locus of all points equidistant from a given point, which is the center of the circle, and a circle can be drawn with a compass. (The phrase "locus of points for a circle" does not seem to be conventionally defined.) or true
How do you find the third vertex of a triangle when given two other points and an area?
You cannot. At least, not one point. If the distance between the two given points is b, and the area of the triangle is A, then let h = 2A/b Then draw two lines parallel to the line formed by the two given points - one above and one below, each of these lines being at a distance h from the first line. Any point on either of these two lines will meet your requirements.
What is A transformation that turns a figure about a fixed point through a given angle and a given direction?
A rotation.
What is a three-dimensional surface in which all points are equidistant from a fixed point?
A 'spherical' surface.
What is the set of points in a plane at a fixed distance from a given point?
CIRCLE
What is the locus of all points that are a fixed distance from a given point?
triangle
What name is given to the set of all points in a plane that are the same distance from a given fixed point?
A circle.
A compass draws all points a given distance from a fixed point thereby creating a locus of points for a circle?
True
The set points in space that are a given distance from a given point is?
In three dimensions, the solid defined as being bound by the set of points at a given distance form a point is a sphere. In two dimensions, the figure defined as being bound by the set of points at a given distance from a point is a circle. In one dimension, a line segment is bound by the two points at a given distance from a point.
Which is a solid bounded by the set of all points at a given distance from a given point?
A sphere is a solid bounded by the set of all points at a given distance from a given point.
The set of all points in a plane that are the same distance from a fixed point?
This set of points forms a circle with the fixed point as its center.
A set of points that are ALL THE same distance from a given point?
The set of all points a given distance from a center point is a circle. The given distance is the radius, and the given point is the center. Or, in 3 dimensional space, a sphere.
What is the mathematical definition of a circle?
A circle is the set of all points in a plane that are a given distance (or a fixed distance) from another point. Take a plane, and then pick any point on it. Then pick a distance from that point you picked and connect all the points that are that distance from your fixed point. That will describe the circumference of a circle. Another idea is to take a plane, pick any point, and then take a compass and put the point of that instrument on that point you picked. Then set a distance on the compass and draw a circle. That circle will be that set of all points a fixed distance from the original point you picked. (A string will work as well as a compass if that string is not stretched to draw the circle.)
What is the locus of points at a given distance from a given point?
A circle
A collection of points in the plane whose distance from fixed point is constant?
That's a circle. The "fixed point" is the center of the circle, and the constant distance is its radius.
What is a point that is equidistant from all points on a circle?
The center of the circle. That's how the circle is defined. (The collection of all points on a plane equidistant from a fixed point. The fixed point is the center and the fixed distance is the radius.)
