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question99
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Would it be correct to say that the distance between particular points is the same as a line? If so, does every possible line on a graph exist? Are the number of lines infinite?
No. A line is a geometric object that extends infinitely far in some direction. If you have two points on a line, the distance between them is a number, often with some units attached such as feet, meters, miles, etc. The portion of the line between the two points is a line seqment.question99 said:Would it be correct to say that the distance between particular points is the same as a line?
I don't know what you mean. By "graph" I assume you mean the graph of some function. If instead of "graph" you mean "coordinate system", then yes, every possible line could be drawn on the coordinate system,question99 said:If so, does every possible line on a graph exist?
Yes.question99 said:Are the number of lines infinite?
No. A line is a geometric object. Distance (between two points) is a mathematical concept and depends on the (mathematical) environment.question99 said:Would it be correct to say that the distance between particular points is the same as a line?
It's the case in Euclide geometryfian said:If you have two points, any lines connecting them are the distance, but the shortest distance is the straight line connecting them.
fian said:If you have two points, any lines connecting them are the distance, but the shortest distance is the straight line connecting them.
Ah, yes. Sorry. I used my daily speaking. You said right about the definition of line.micromass said:No, a distance is not a line. A line is a geometrical objects consisting of an infinite number of points. A distance is a number. So you should phrase it has "the shortest path is the straight line connecting them" or "the shortest distance is measured along the straight line connecting them"
Mark44 said:I don't know what you mean. By "graph" I assume you mean the graph of some function. If instead of "graph" you mean "coordinate system", then yes, every possible line could be drawn on the coordinate system,
All of the concepts of geometry, including lines, points, circles, and so on, are abstract concepts. A geometric line has infinite length but its width is zero. Whenever we use a pen or pencil to draw a line on graph paper, what we make is only an approximation to a geometric line. I wouldn't say that we are doing this illegally, though.Vinay080 said:But, isn't line a abstract (something not representing or imitating external reality) idea? I thought we can't draw a line on the (cartesian) coordinate system (consisting of abstract lines as axis'), though we draw them illegally!
I might require a new thread to deal with this, but thank you for clarification Mark44.I wouldn't say that we are doing this illegally, though.
A line is a geometric figure that extends infinitely in both directions and is perfectly straight. It is often represented by a straight, thin line with two arrowheads on each end.
Distance is the measurement of how far apart two points are. It is usually measured in units such as meters, feet, or miles.
No, a line and distance are not the same. A line is a geometric figure, while distance is a measurement of the space between two points.
Lines can be used to represent distance, as they extend infinitely in both directions and do not have an endpoint. Distance is also often used to describe the length of a line segment, which is a portion of a line between two endpoints.
Yes, a line can have a distance. The length of a line is a measurement of its distance, and it can be calculated using various formulas, such as the distance formula or Pythagorean theorem.