Question

label a ray with endpoint z. determine an appropriate name for a ray whose endpoint is z.

choose the correct ray whose endpoint is z.

a. diagram with w and z, double arrow

b. diagram with w and z, no arrow

c. diagram with z and w, left arrow

d. diagram with z and w, right arrow

Explanation:

A ray has one endpoint and extends infinitely in one direction. The endpoint is the first letter in the ray's name, and the second letter indicates the direction of extension.

• Option A: This is a line (extends infinitely in both directions), not a ray.
• Option B: This is a segment (has two endpoints, no infinite extension).
• Option C: The endpoint here would be \( W \) (since the arrow is from \( Z \) to \( W \) direction? No, the arrow is leftward from \( Z \), but the first point should be the endpoint. Wait, no—for a ray, the endpoint is the starting point, and the ray goes through the second point. So in option C, the ray is drawn with \( Z \) first and arrow towards the left (past \( Z \)? No, the points are \( Z \) and \( W \), with arrow left from \( Z \). Wait, no, the ray's name should have the endpoint first. So if the endpoint is \( Z \), the ray should go through another point (like \( W \)) in one direction. Let's check each:
• Option D: The endpoint is \( Z \) (first point), and the ray goes through \( W \) and extends to the right (arrow at \( W \) end, so direction is \( Z \) to \( W \) to infinity). So this is a ray with endpoint \( Z \), named \( \overrightarrow{ZW} \).
• Option C: The ray is drawn with \( Z \) and \( W \), arrow to the left (from \( Z \) towards left, past \( Z \)? No, the points are \( Z \) and \( W \), arrow left from \( Z \), so the endpoint would be \( Z \), but the direction is left, so the ray would be \( \overrightarrow{Z} \) (but no, the second point should be in the direction. Wait, no—if the arrow is left, the ray starts at \( Z \) and goes left, but the other point is \( W \) to the right of \( Z \). That doesn't make sense. So option D: starts at \( Z \), goes through \( W \), and extends right (arrow at \( W \) end), so that's a ray with endpoint \( Z \), direction through \( W \).

Answer:

D. \( \boldsymbol{\cdot Z \quad \cdot W
ightarrow} \) (or described as the ray with endpoint \( Z \), passing through \( W \) and extending to the right)