Question

For every line L and for every point P not lying on a given line L, there exists _____________ passing through P and parallel to L.

• A. no line
• B. a unique
• C. two lines
• D. infinitely many lines

Answer 1

Answer: (B)

a unique

The answer is B i.e., a unique line.

It is based on the Playfair axiom.

In geometry, Playfair's axiom is an axiom that can be used instead of the fifth postulate of Euclid (the parallel postulate):

In a plane, given a line and a point not on it, at most one line parallel to the given line can be drawn through the point.