2007-06-13 10:00:16 · 11 answers · asked by Alexander 6 in Science & Mathematics ➔ Mathematics
one parallel
2007-06-13 10:02:28 · answer #1 · answered by Pengy 7 · 0⤊ 0⤋
1
2007-06-13 17:03:13 · answer #2 · answered by BG 3 · 0⤊ 0⤋
Remember, in Euclidean geometry, a line is an infinite number of points that extends in both directions infinitely.
That being the case, given an arbitrary point A and a line B, there can only exist a single line through point A, not intersecting line B. This line is the parallel line through point A by definition. All other lines will at one point or another intersect line B.
2007-06-13 17:05:08 · answer #3 · answered by Shiver 2 · 0⤊ 0⤋
Are you studying non-euclidean geometry?
The essential difference between Euclidean and non-Euclidean geometry is the nature of parallel lines. Euclid's 5th postulate is equivalent to stating that, within a two-dimensional plane, for any given line l and a point A, which is not on l, there is exactly one line through A that does not intersect l. In hyperbolic geometry, by contrast, there are infinitely many lines through A not intersecting l, while in elliptic geometry, any pair of lines intersect.
2007-06-13 17:11:14 · answer #4 · answered by mathjoe 3 · 0⤊ 0⤋
If the point A is on the straight line b, then the answer is 0; otherwise answer is 1 (that is parallel to the given straight line).
2007-06-13 17:04:38 · answer #5 · answered by Sanny 2 · 0⤊ 0⤋
If we assume Euclidean geometry and two dimensions the answer is 1 line and it is parallel. In three or more dimensions you can have an infinite number of skew lines thru point A that do not intersect line b.
2007-06-14 05:18:27 · answer #6 · answered by Northstar 7 · 0⤊ 0⤋
One. For the two lines to never intersect, they have to be parallel, and there is only one set of parallel lines for lines drawn through defined points.
2007-06-13 17:03:45 · answer #7 · answered by JLynes 5 · 0⤊ 0⤋
You guys need to think outside the box, or should I say "outside the plane?" There is 1 line through A that would be parallel to b, but an infinite number that could be skew (noncoplanar) to b and therefore not intersect b.
2007-06-13 17:06:32 · answer #8 · answered by Kathleen K 7 · 0⤊ 0⤋
one, the line going through A is parallel to line b
2007-06-13 17:03:31 · answer #9 · answered by Ziggy 3 · 0⤊ 0⤋
If we are limited to a single plane:
..If point A is not on b: 1 line, parallel to b
..If point A is on b: no such lines
If we are not limited to a single plane: infinitely many
If the geometry of our plane is not Eucledian, but Lobachevski: no such lines
2007-06-13 17:08:11 · answer #10 · answered by iluxa 5 · 1⤊ 0⤋