Question

use the picture to name four rays.

a) \\( \overrightarrow { s t }, \overrightarrow { s w }, \overrightarrow { s u }, \overrightarrow { u v } \\)
b) \\( \overrightarrow { v t }, \overrightarrow { v w }, \overrightarrow { w u }, \overrightarrow { v s } \\)
c) \\( \overrightarrow { s t }, \overrightarrow { t u }, \overrightarrow { t v }, \overrightarrow { t w } \\)
d) \\( \overrightarrow { w s }, \overrightarrow { w t }, \overrightarrow { w u }, \overrightarrow { v w } \\)

Explanation:

Step1: Recall the definition of a ray

A ray has one endpoint and extends infinitely in one direction.

Step2: Analyze each option

• Option A: \(\overrightarrow{ST}\) has endpoint \(S\) and goes through \(T\), \(\overrightarrow{SW}\) has endpoint \(S\) and goes through \(W\), \(\overrightarrow{SU}\) has endpoint \(S\) and goes through \(U\), but \(\overrightarrow{UV}\) has endpoint \(U\) and goes through \(V\) which is not in line with the ray - naming convention for the given figure's main structure.
• Option B: \(\overrightarrow{VT}\) has endpoint \(V\) and goes through \(T\), \(\overrightarrow{VW}\) has endpoint \(V\) and goes through \(W\), \(\overrightarrow{WU}\) has endpoint \(W\) and goes through \(U\), \(\overrightarrow{VS}\) has endpoint \(V\) and goes through \(S\). These rays are well - defined according to the ray definition.
• Option C: \(\overrightarrow{ST}\) is correct, \(\overrightarrow{TU}\) is a line segment (has two endpoints \(T\) and \(U\), not a ray), so this option is incorrect.
• Option D: \(\overrightarrow{WS}\) has endpoint \(W\) and goes through \(S\), \(\overrightarrow{WT}\) has endpoint \(W\) and goes through \(T\), \(\overrightarrow{WU}\) has endpoint \(W\) and goes through \(U\), \(\overrightarrow{VW}\) has endpoint \(V\) and goes through \(W\). But the naming of rays in the figure, the rays from \(V\) to \(T\) and \(V\) to \(S\) are more prominent in the fence - like structure than just \(\overrightarrow{VW}\) in this combination.

Answer:

B. \(\overrightarrow{VT},\overrightarrow{VW},\overrightarrow{WU},\overrightarrow{VS}\)