Question

if rs = 7, rt = 5, st = 12, and points r, s, and t are collinear, what is the relationship between points r, s, and t? a) there is not enough information to determine the relationship. b) point r is between point s and point t. c) point s is between point r and point t. d) point t is between point r and point s.

Explanation:

To determine the relationship between collinear points \( R \), \( S \), and \( T \), we use the segment addition postulate. If a point is between two other points, the sum of the two smaller segments should equal the largest segment.

Given:

• \( RS = 7 \)
• \( RT = 5 \)
• \( ST = 12 \)

We check the sums:

• If \( R \) is between \( S \) and \( T \), then \( SR + RT = ST \). Let's verify: \( SR = RS = 7 \), so \( 7 + 5 = 12 \), which equals \( ST \). This satisfies the segment addition postulate.

Let's check the other options:

• For option C ( \( S \) between \( R \) and \( T \) ), we would need \( RS + ST = RT \), but \( 7 + 12 = 19

eq 5 \), so this is false.

• For option D ( \( T \) between \( R \) and \( S \) ), we would need \( RT + TS = RS \), but \( 5 + 12 = 17

eq 7 \), so this is false.

• Option A is incorrect because we have enough information to determine the relationship.

Answer:

B) Point \( R \) is between point \( S \) and point \( T \).