I'm mixed on this question. Since one point could be on infinite many planes... does that apply to five points too?
2007-09-16 16:38:41 · 9 answers · asked by Sai 1 in Science & Mathematics ➔ Mathematics
If the five points are on the same line, then they must be on the same plane. However, it will be impossible to identify a single plane to which they belong, as a line can be on many planes.
Take one of the points and draw a vector at 90 degrees from the line. You can have a plane that will contain the 5-point line and the vector.
However, the vector can be rotated around the line (360 degrees worth) and at any angle where you stop it, you will have a plane that contains the line and the vector.
You can have as many planes as you can find distinct angles around the line.
2007-09-16 16:46:11 · answer #1 · answered by Raymond 7 · 0⤊ 0⤋
The five points are coplanar. The line they lie on is part of a infinite number of planes. But in each case, all the points lie on the same plane.
2007-09-16 22:27:36 · answer #2 · answered by Staara 3 · 0⤊ 0⤋
Yes, each point is on infinite planes, but since a line does not curve, all points on a single line are coplanar.
2007-09-16 16:46:37 · answer #3 · answered by ccw 4 · 0⤊ 0⤋
N points that lie on the same line will all lie in ANY plane that contains that line. So yes, they are coplanar too.
2007-09-16 16:44:16 · answer #4 · answered by Anonymous · 0⤊ 0⤋
Collinear means they form a straight line. Start with any one point. You can draw four lines by connecting it to each of the other four points. Now select a second point. It is already connected to the first point so you can only form three new lines. The third point only gives two new lines and the fourth gives one. So the total is 4 + 3 + 2 + 1 = 10
2016-05-21 06:51:57 · answer #5 · answered by ? 3 · 0⤊ 0⤋
not only are they coplanar, but they are coplanar in infinite planes, because all points lie on the same line, which lies in infinite planes.
2007-09-16 22:24:09 · answer #6 · answered by Anonymous · 0⤊ 0⤋
3 points are always coplanar...4 points may or may not be coplanar...
draw a straight l ine with 5 points. its coplanar.
draw 3 points. close it. there would only be one flat plane...but if you draw another point anywhere...it'll have one or two planes(its best to check the coordinates).
2007-09-16 16:54:18 · answer #7 · answered by Anonymous · 0⤊ 0⤋
Yes. If they're on the same line, then they are on an infinite number of the same planes (imagine all possible planes rotating around the line).
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2007-09-16 16:44:40 · answer #8 · answered by tsr21 6 · 0⤊ 0⤋
YES, they are coplanar
2007-09-17 01:48:12 · answer #9 · answered by rose chandana k 1 · 0⤊ 0⤋