Question

if points n, u, and t are collinear, name all the segments they determine.

Explanation:

Step 1: Recall the definition of a segment

A segment is a part of a line with two endpoints. For collinear points \( K \), \( N \), \( U \), \( T \) (lying on the same line), we find all pairs of these points to form segments.

Step 2: List all pairs of points

• Pairs with \( K \): \( (K, N) \), \( (K, U) \), \( (K, T) \) which form \( \overline{KN} \), \( \overline{KU} \), \( \overline{KT} \).
• Pairs with \( N \) (excluding \( K \) as already considered): \( (N, U) \), \( (N, T) \) which form \( \overline{NU} \), \( \overline{NT} \).
• Pair with \( U \) (excluding \( K, N \) as already considered): \( (U, T) \) which forms \( \overline{UT} \).

Answer:

The segments determined by collinear points \( K \), \( N \), \( U \), and \( T \) are \( \overline{KN} \), \( \overline{KU} \), \( \overline{KT} \), \( \overline{NU} \), \( \overline{NT} \), and \( \overline{UT} \).