Question

planes a and b are shown
if a new line, p, is drawn parallel to line l, which
statement is true?
line p must be drawn in plane b
line p must be perpendicular to line m
line p must be drawn so that it can lie in the same
plane as line l
line p must be drawn in the same plane as line n

Explanation:

Step1: Analyze properties of parallel lines

Parallel lines are coplanar. If line \( p \) is parallel to line \( l \), by the definition of parallel lines in Euclidean geometry, they must lie in the same plane.

Step2: Analyze each option

• Option 1: Line \( p \) does not must be drawn in plane \( B \). It can be in another plane as long as it is parallel to \( l \) and in the same plane as \( l \).
• Option 2: There is no information to suggest that line \( p \) must be perpendicular to line \( m \). Just because \( p\parallel l \), and \( l \) and \( m \) are in a plane (maybe intersecting or not in a perpendicular - way shown in the general diagram), this is not a valid conclusion.
• Option 3: Correct as per the property of parallel lines (coplanar).
• Option 4: Line \( p \) is parallel to \( l \), and there is no relation given (from the general parallel - line property) that it must be in the same plane as line \( n \). Line \( n \) is in a different plane (intersecting the plane of \( l \) and \( m \)).

Answer:

Line \( p \) must be drawn so that it can lie in the same plane as line \( l \).