The geometric term that best describes a straight path between two points is a "line segment." A line segment has two endpoints and represents the shortest distance between those points. Unlike a line, which extends infinitely in both directions, a line segment has a defined length.
By the geometric definition of a line, it is represented by two points, and all points on the line are collinear, between or extrapolating to infinity from the straight line made by the two points. In other words, a line is straight, and can be represented by a binomial function (example: y=2x+1). A parabola is a function, but cannot be described mathematically as a line.
The geometric term you are describing is a "line." A line is defined as an infinite set of points that extends indefinitely in both directions, possessing length but no width or thickness. It is one of the fundamental concepts in geometry and is often represented visually as a straight path connecting two points.
It could be a circle or a sphere
The statement is not accurate; while straight lines, circles, and angle bisectors are indeed defined by loci of points, many other geometric objects can also be described this way. For instance, ellipses and parabolas are defined by specific loci of points relative to focal points. Additionally, more complex shapes, such as polygons and curves, can also be defined using the concept of loci, depending on the conditions set for the points. Thus, the locus points idea applies to a broader range of geometric objects than just the ones mentioned.
Collinear points are two or more points that lie on the same straight line. This means that if you can draw a straight line through the points without any deviations, they are considered collinear. In a geometric context, determining if points are collinear can be done using various methods, such as calculating the slope between pairs of points.
By the geometric definition of a line, it is represented by two points, and all points on the line are collinear, between or extrapolating to infinity from the straight line made by the two points. In other words, a line is straight, and can be represented by a binomial function (example: y=2x+1). A parabola is a function, but cannot be described mathematically as a line.
It is an collection of an infinite number of points.
The geometric term you are describing is a "line." A line is defined as an infinite set of points that extends indefinitely in both directions, possessing length but no width or thickness. It is one of the fundamental concepts in geometry and is often represented visually as a straight path connecting two points.
No, they are not the only geometric objects.
It could be a circle or a sphere
The statement is not accurate; while straight lines, circles, and angle bisectors are indeed defined by loci of points, many other geometric objects can also be described this way. For instance, ellipses and parabolas are defined by specific loci of points relative to focal points. Additionally, more complex shapes, such as polygons and curves, can also be defined using the concept of loci, depending on the conditions set for the points. Thus, the locus points idea applies to a broader range of geometric objects than just the ones mentioned.
Collinear points are two or more points that lie on the same straight line. This means that if you can draw a straight line through the points without any deviations, they are considered collinear. In a geometric context, determining if points are collinear can be done using various methods, such as calculating the slope between pairs of points.
The metric of a geometric space is defined as the distance between two points.
False, other geometric objects exist which can be defined as a parrticular locus of points, such as the parabola and the hyperbola.
line segment
An ellipse? The shape described is not an exactly describable geometric shape, (), and as far as I know there is no name for it.
Lines that are described as a straight continuous arrangement of an infinite number of points are known as geometric lines in mathematics. These lines extend infinitely in both directions and have no width or thickness, consisting solely of a series of points that are collinear. In Euclidean geometry, lines can be defined by two distinct points or by a linear equation. They are fundamental concepts in geometry, serving as the basis for more complex shapes and figures.