planes a and b are shown.\nif a new line, p, is drawn parallel to line l, which statement is true?\nline p…
planes a and b are shown.\nif a new line, p, is drawn parallel to line l, which statement is true?\nline p must be drawn in plane b.\nline p must be perpendicular to line m.\nline p must be drawn so that it can lie in the same plane as line l.\nline p must be drawn in the same plane as line n.
Answer
Explanation:
Step1: Recall Parallel Line Properties
Parallel lines must lie in the same plane (coplanar) and never intersect.
Step2: Analyze Each Option
- Option 1: Line ( p ) parallel to ( l ) doesn't have to be in plane ( B ); ( l ) is in plane ( A ), so ( p ) can be in a plane with ( l ), not necessarily ( B ). Eliminate.
- Option 2: No info shows ( l ) is perpendicular to ( m ), so ( p \parallel l ) doesn't imply ( p \perp m ). Eliminate.
- Option 3: Parallel lines are coplanar, so ( p \parallel l ) means ( p ) must lie in the same plane as ( l ) (or a parallel plane, but "can lie in the same plane" is true as they must be coplanar). This is correct.
- Option 4: Line ( n ) is in plane ( B ), ( l ) in ( A ); ( p \parallel l ) doesn't need to be in plane ( B ) (with ( n )). Eliminate.