Question

1. in the diagram below, which two rays are opposite one another? diagram with points m, q, p, n, x options: $overrightarrow{xq}$ and $overrightarrow{mn}$; $overrightarrow{px}$ and $overrightarrow{xn}$; $overrightarrow{xm}$ and $overrightarrow{xn}$; $overrightarrow{mn}$ and $overrightarrow{pq}$

Explanation:

To determine opposite rays, they must share the same endpoint and form a straight line (collinear, extending in opposite directions).

• Analyze each option:
• Option 1: $\overrightarrow{XQ}$ and $\overrightarrow{MN}$ – Different endpoints (X vs M), not opposite.
• Option 2: $\overrightarrow{PX}$ and $\overrightarrow{XN}$ – Different directions (PX starts at P, XN at X), not sharing the same endpoint in a way to form a straight line.
• Option 3: $\overrightarrow{XM}$ and $\overrightarrow{XN}$ – Share endpoint X, lie on the same line (MN) and extend in opposite directions (M and N are opposite along the line through X).
• Option 4: $\overrightarrow{MN}$ and $\overrightarrow{PQ}$ – Different lines (intersecting at X but not colinear in a way to be opposite rays).

Answer:

C. $\boldsymbol{\overrightarrow{XM}}$ and $\boldsymbol{\overrightarrow{XN}}$ (Note: Assuming the third option is labeled C; adjust label based on original question's numbering if needed, but the rays $\overrightarrow{XM}$ and $\overrightarrow{XN}$ are opposite as they share endpoint X and form a straight line in opposite directions.)