Question
Is point S between points R and T? Given: Points S, R, and T are collinear. Also, mRS =6, mRT =4, and mST =10
Answers
GPT-4o mini
To determine if point \( S \) is between points \( R \) and \( T \), we need to analyze the distances given:
1. \( mRS = 6 \): This means the distance from \( R \) to \( S \) is 6 units.
2. \( mRT = 4 \): This means the distance from \( R \) to \( T \) is 4 units.
3. \( mST = 10 \): This means the distance from \( S \) to \( T \) is 10 units.
Since we know the distances from \( R \) to \( S \), \( R \) to \( T \), and \( S \) to \( T \), we can evaluate their positions:
- If point \( S \) is between points \( R \) and \( T \), then the following relationship should hold true:
\[
mRS + mST = mRT
\]
- Substituting the values:
\[
6 + 10 = 4
\]
However, \( 6 + 10 = 16 \), which does not equal \( 4 \).
This inconsistency indicates that point \( S \) cannot be between \( R \) and \( T \). Instead, the distances imply that:
- \( R \) is 4 units away from \( T \),
- \( S \) is beyond \( T \), since the distance \( ST \) (10) plus the distance \( RT \) (4) gives a total distance of 14 from \( R \) to \( T \) additively, which supports that \( R \) and \( T \) are closer together than \( S \) to \( T \).
Therefore, **point \( S \) is not between points \( R \) and \( T \)**. In fact, point \( S \) is beyond point \( T \) along the line defined by points \( R \), \( S \), and \( T \).
1. \( mRS = 6 \): This means the distance from \( R \) to \( S \) is 6 units.
2. \( mRT = 4 \): This means the distance from \( R \) to \( T \) is 4 units.
3. \( mST = 10 \): This means the distance from \( S \) to \( T \) is 10 units.
Since we know the distances from \( R \) to \( S \), \( R \) to \( T \), and \( S \) to \( T \), we can evaluate their positions:
- If point \( S \) is between points \( R \) and \( T \), then the following relationship should hold true:
\[
mRS + mST = mRT
\]
- Substituting the values:
\[
6 + 10 = 4
\]
However, \( 6 + 10 = 16 \), which does not equal \( 4 \).
This inconsistency indicates that point \( S \) cannot be between \( R \) and \( T \). Instead, the distances imply that:
- \( R \) is 4 units away from \( T \),
- \( S \) is beyond \( T \), since the distance \( ST \) (10) plus the distance \( RT \) (4) gives a total distance of 14 from \( R \) to \( T \) additively, which supports that \( R \) and \( T \) are closer together than \( S \) to \( T \).
Therefore, **point \( S \) is not between points \( R \) and \( T \)**. In fact, point \( S \) is beyond point \( T \) along the line defined by points \( R \), \( S \), and \( T \).