What is the intersection of two coplanar lines?
The correct answer and explanation is:
The intersection of two coplanar lines is a point, provided the lines are not parallel. If two lines lie on the same plane, they either meet at a single point or do not meet at all if they are parallel.
To understand this concept, consider two lines in a plane. A plane is a flat, two-dimensional surface that extends infinitely in all directions. Two lines that are coplanar must be located on the same plane. If the lines are not parallel, they will eventually intersect at one point, because in two dimensions, two non-parallel lines can only meet at one place. This is a result of the lines being distinct but not having the same slope, which forces them to cross each other at a particular point.
However, if the lines are parallel, they will never intersect. Parallel lines have the same slope and maintain a constant distance from each other, meaning they will not meet, regardless of how far they are extended.
In geometric terms, the intersection of two lines in a plane can be determined by solving their respective equations. If the system of equations has a solution, the lines intersect at a point corresponding to that solution. If no solution exists, the lines do not intersect, implying they are parallel.
For non-parallel lines, the intersection point is unique. This is a fundamental property of Euclidean geometry, where two distinct lines in a plane can intersect at most at one point. Therefore, the intersection of two coplanar lines is always a point unless the lines are parallel.