To answer this question, let's first clarify what it means for two rays to be the same. A ray is defined by its starting point (the endpoint) and a direction through another point. For example, ray \( QL \) is a ray that starts at \( Q \) and goes through \( L \) and beyond in that direction.
Here are the pairs considered one by one:
A. \( QL⎯→⎯ \) and \( LQ⎯→⎯ \)
- **Not correct**: Ray \( QL \) starts at \( Q \) and passes through \( L \). Ray \( LQ \) starts at \( L \) and passes through \( Q \). These are not the same rays because they start at different points.
B. \( QP⎯→⎯⎯ \) and \( PL⎯→⎯ \)
- **Not correct**: Ray \( QP \) starts at \( Q \) and passes through \( P \), and ray \( PL \) starts at \( P \) and passes through \( L \). These two rays are not the same as they start at different points and pass through different sequences of points.
C. \( LP⎯→⎯ \) and \( PQ⎯→⎯⎯ \)
- **Not correct**: Ray \( LP \) starts at \( L \) and passes through \( P \), and ray \( PQ \) starts at \( P \) and passes through \( Q \). Again, these rays start at different points and hence are different rays.
D. \( QP⎯→⎯⎯ \) and \( QL⎯→⎯ \)
- **Not correct**: Ray \( QP \) starts at \( Q \) and passes through \( P \), and ray \( QL \) starts at \( Q \) and passes through \( L \). These rays have the same starting point but pass through different points, so they are different rays.
None of the given pairs represent two different names for the same ray. Therefore, there seems to be a problem with the provided answer options as none of them define the same ray under different names.
Think about the number of rays in this figure. Next, think about how many of these rays can be named using the points that are already labeled.
Which of the following pairs represents two different names for the same ray?
A.
QL⎯→⎯ and LQ⎯→⎯
B.
QP⎯→⎯⎯ and PL⎯→⎯
C.
LP⎯→⎯ and PQ⎯→⎯⎯
D.
QP⎯→⎯⎯ and QL⎯→⎯
Check Answer
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