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In Euclidean geometry if there is a line and a point not on the line then there is exactly one line through the point and the parallel to the given line. True or false?
True. In Euclidean geometry, if there is a line and a point not on that line, there exists exactly one line that can be drawn through the point that is parallel to the given line. This is known as the Parallel Postulate, which states that for a given line and a point not on it, there is one and only one line parallel to the given line that passes through the point.
Do Through a point not on a line one and only one line always can be drawn parallel to the given line?
True
Only one plane can pass through one line and a point that is not on the line?
I'd feel a lot more comfortable if you said "... can contain one line and a point ...".When you say "pass through one line", I picture a sword passing through a tight pieceof string. If that's how your plane passes through the line, then the statement in your"question" is false. If your plane contains the line and the extra point, then the statementis true ... only one plane can do that.
What is Euclid's parallel postulate?
Although he presented it differently, the modern version is as follows:given a straight line and a point which is not on that line, there is only one line which will pass through the point and which is parallel to the line.
How do you graph a line with one point?
If you're only given one point, you can't draw the graph of the line, because there are an infinite number of different lines that all go through that one point. Or, to put it another way, if someone gives you a single point and asks you to draw the line through it, you can draw any old line you want through that point, and nobody can say it's wrong. In order to pin it down to one unique line, you need another piece of information in addition to the one point: either the slope of the line, or another point.
Can only one plane pass through one line and a point that is not on the line?
Yes
What is needed to determine a line?
Two points determine a line. Also there is one and only line perpendicular to given line through a given point on the line,. and There is one and only line parallel to given line through a given point not on the line.
Do Through a point not on a line one and only one line always can be drawn parallel to the given line?
True
Is it true that only one plane can pass through one and a point that is not on the line?
If you mean "only one plane can pass through another plane and through a point that is not on the line formed by the intersection of the two planes," the answer is "no." If you rotate the plane about the point, it will still intersect the line unless it is parallel to the line. By rotating the plane, you have created other planes that pass through the unmoved plane and through the point that is not on the line formed by the intersection of the two planes.
Only one plane can pass through one line and a point that is not on the line?
I'd feel a lot more comfortable if you said "... can contain one line and a point ...".When you say "pass through one line", I picture a sword passing through a tight pieceof string. If that's how your plane passes through the line, then the statement in your"question" is false. If your plane contains the line and the extra point, then the statementis true ... only one plane can do that.
What is Euclid's parallel postulate?
Although he presented it differently, the modern version is as follows:given a straight line and a point which is not on that line, there is only one line which will pass through the point and which is parallel to the line.
How do you graph a line with one point?
If you're only given one point, you can't draw the graph of the line, because there are an infinite number of different lines that all go through that one point. Or, to put it another way, if someone gives you a single point and asks you to draw the line through it, you can draw any old line you want through that point, and nobody can say it's wrong. In order to pin it down to one unique line, you need another piece of information in addition to the one point: either the slope of the line, or another point.
Properties of a slope?
The slope of a line can be determined by examining the graph; only one line through a point has a particular slope.
If a plane contains one point of a line then it must contain the entire line?
No, a plane can contain only one point of a line. Picture a piece of paper with a pencil stabbed through it. The paper is the plane, and the pencil is the line. The pencil/line only touches the paper/plane at one point. Hope this helped! If it did, please recommend me. -Brad
What criteria must be met for a line to be considered a function?
A line must pass the vertical line test to be considered a function. This means that a vertical line drawn through any point on the line will only intersect the line at one point, indicating that each input has only one output.
How do you construct a line tangent through a circle through a point outside the circle?
The tangent line only touches the outside of a circle at one given point. So an outside line perpendicular to the circle's diameter at 90 degrees should do.
How many lines can be drawn through one point?
uncountable lines can be drawn through one point.
