Final answer:
There is exactly one line that can be drawn parallel to a given line l through a point not on line l, based on the Euclidean geometry postulate. The correct answer is A.
Step-by-step explanation:
In geometry, when a line passes through a point not on line l, there is exactly one line that can be drawn that is parallel to line l. This is based on the Euclidean geometry postulate which states that for any given line and a point not on that line, there exists exactly one line through the point that does not intersect the original line, hence is parallel to it. This concept is often encountered in middle school geometry classes.
To visualize this, imagine line l as a straight line on a piece of paper and a point P that is not on line l. Now, by using a ruler or any straightedge, you can draw a line through P that doesn't touch line l. You'll find that only one such line can exist that remains parallel to line l at all points.
This is the foundation of parallel lines in Euclidean space, and it does not depend on the location of the point as long as the point is not on line l. Two lines are parallel if they are always the same distance apart (equidistant) and will never meet. No matter how the lines are extended, they will never intersect. This property of lines is fundamental in geometry, and helps to solve various problems and prove many theorems.