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 $S$, $\overrightarrow{SW}$ has endpoint $S$, $\overrightarrow{SU}$ has endpoint $S$, $\overrightarrow{UV}$ has endpoint $U$. But in the figure, rays should start from appropriate points.
• Option B: $\overrightarrow{VT}$ has endpoint $V$, $\overrightarrow{VW}$ has endpoint $V$, $\overrightarrow{WU}$ has endpoint $W$ (not a valid ray as per the figure's structure), $\overrightarrow{VS}$ has endpoint $V$.
• Option C: $\overrightarrow{ST}$ has endpoint $S$, $\overrightarrow{TU}$ has endpoint $T$, $\overrightarrow{TV}$ has endpoint $T$, $\overrightarrow{TW}$ has endpoint $T$. These are all valid rays as per the figure.
• Option D: $\overrightarrow{WS}$ has endpoint $W$, $\overrightarrow{WT}$ has endpoint $W$, $\overrightarrow{WU}$ has endpoint $W$, $\overrightarrow{VW}$ has endpoint $V$.

Answer:

C. $\overrightarrow{ST}$, $\overrightarrow{TU}$, $\overrightarrow{TV}$, $\overrightarrow{TW}$