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Why can three coplanar lines have zero one two or three points of intersection?
If all three lines are parallel, there are zero points of intersection. If all three lines go through a point, there is one point of intersection. If two lines are parallel and the third one crosses them, there are two. If the three lines make a triangle, there are three points.
What is the number of points at which two parallel lines intersect?
Parallel lines NEVER touch, so zero.
What system of equations has no solution?
A system of equations will have no solutions if the line they represent are parallel. Remember that the solution of a system of equations is physically represented by the intersection point of the two lines. If the lines don't intersect (parallel) then there can be no solution.
Can four lines have only two intersection points?
No, four lines can can have 6 total intersections. They would be Ab, Ac, Ad, Bc, Bd, and Cd
What is the locus of points at a given distance of a line?
The locus of points at a given distance to a line would be a line parallel to the first line. Assuming that both lines are straight.
