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How do you draw two lines that intersect and another line that does not intersect either one?
Wiki User
∙ 14y ago
If you mean that the lines intersect in a point then it can't be done. At least not in a plane assuming Euclidean geometry.
Proof:
We draw up a system of coordinates on the plane so that the two first intersecting lines can be represented by the equations
- y1 = ax + b
- y2 = cx + d
Since the lines intersect in a point a must not equal c, since those numbers determine the relative angle of the lines, and if a = c the line would be parallel - thus never intersect - or they would intersect in all points along any of the lines.
Now, to introduce another line which neither intersects y1 nor y2, we set up the following:
- y3 = ex + f
- In order for y3 to not intersect y1 it has to be parallel to it, i.e. e = a must be true
- In order for y3 to not intersect y2 it has to be parallel to that, too, i.e. e = c must be true
Together with what we established earlier, that a =/= c we can easily see the impossibility in e = a being true at the same time as e = c. Thus the third line must intersect at least one other line.
QED
Wiki User
∙ 14y ago
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