Two lines can intersect at none, one or infinitely many points.
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Yes, perpendicular lines do intersect at a single point. Think of the line representing the x-axis, and the line representing the y-axis. These two lines are perpendicular, and they intersect at the Origin (a single point).
No, two straight lines can intersect at only one point and that is their point of intersection.
When two lines intersect they form an axes.
Two lines cross or intersect at a point.
If they do intersect, it will be at their point of intersection.