Planes A and B are shown.
m
72
B
IA
If a new line, p, is drawn parallel to line /, which statement is true?
A. Line p must be drawn in plane B.
B. Line p must be perpendicular to line m.
C. Line p must be drawn so that it can lie in the same plane as line 1.
D. Line p must be drawn in the same plane as line n.
Answer (2)
The correct statement regarding line p, which is parallel to line l, is that it must be able to lie in the same plane as line l. Hence, the answer is option C. The other options do not hold true based on the definitions of parallel and perpendicular lines.
;
To solve this problem, we need to understand the relationship between the lines and planes in the given scenario.
Let's analyze the provided statements:
Line p must be drawn in plane B.
This statement is not necessarily true. For two lines to be parallel, they do not have to be in the same plane. They need to have the same direction and never intersect even if extended infinitely. Thus, line p does not have to be in plane B specifically.
Line p must be perpendicular to line m.
This statement is false because if line p is to be parallel to line l, it should never intersect line l and should have the same direction as line l. Thus, it cannot be perpendicular to line m unless this aligns with line l's orientation, which we are not given information about.
Line p must be drawn so that it can lie in the same plane as line l.
This is the correct statement, as for two lines to be parallel, they can either be in the same or parallel planes while maintaining the property of having the same direction and not intersecting each other.
Line p must be drawn in the same plane as line n.
Without further information about line n, we cannot assume this statement to be true. Thus, it cannot be definitively determined that line p must be drawn in the same plane as line n.
Given these analyses, the correct statement is that line p must be drawn so that it can lie in the same plane as line l.
