Question

name the figure below in two different ways.

Explanation:

Step1: Identify the figure type

The figure is a ray. A ray starts at a point and extends infinitely in one direction.

Step2: Name using endpoint and another point

One way is to use the endpoint first, then another point on the ray. So, ray \( YE \) (starting at \( Y \), passing through \( S \) and \( E \), extending beyond \( E \)). Another way is ray \( YS \) (but wait, actually, since it goes through \( S \) to \( E \), more accurately, ray \( YE \) and also, since \( S \) is on the ray from \( Y \) through \( E \), we can also consider the ray as starting at \( Y \), so ray \( YS \) is part of it, but the standard way is to use the endpoint and a point in the direction of extension. Wait, the figure has \( Y \) as the endpoint, \( S \) in between, and \( E \) at the other end (but actually, a ray has one endpoint and extends infinitely, so maybe the figure is a ray with endpoint \( Y \), passing through \( S \) and \( E \), so it can be named as ray \( YE \) (using endpoint \( Y \) and point \( E \) on the ray) and also, since \( S \) is on the ray, we can name it as ray \( YS \) (but actually, the correct two ways are using the endpoint and any other point on the ray. So first, ray \( YE \) (endpoint \( Y \), direction towards \( E \)) and second, ray \( YS \) (endpoint \( Y \), direction towards \( S \), but since \( S \) is between \( Y \) and \( E \), the ray \( YS \) is the same as ray \( YE \) in terms of the ray (since a ray is defined by its endpoint and direction). Wait, maybe the figure is a line segment? No, it has an arrow at \( Y \)? Wait, looking at the diagram, \( Y \) has an arrow, \( E \) has a dot, \( S \) is a dot in between. So it's a ray with endpoint \( Y \), passing through \( S \) and \( E \), extending infinitely beyond \( E \)? Wait, no, the arrow is at \( Y \), so maybe the ray is from \( Y \) through \( S \) to \( E \), with \( Y \) as the endpoint, and extending towards \( E \) (but the arrow is at \( Y \), which is confusing. Wait, maybe it's a ray with endpoint \( Y \), so the ray is \( \overrightarrow{YE} \) (vector notation, but ray notation is \( \overrightarrow{Y E} \) or \( \text{Ray } YE \)) and also, since \( S \) is on the ray, \( \overrightarrow{YS} \) (Ray \( YS \)). But actually, the two ways to name a ray are by its endpoint and any other point on the ray. So the ray can be named as Ray \( YE \) (using endpoint \( Y \) and point \( E \)) and Ray \( YS \) (using endpoint \( Y \) and point \( S \)).

Answer:

The figure (a ray) can be named as \(\boldsymbol{\text{Ray } YE}\) and \(\boldsymbol{\text{Ray } YS}\) (or using the symbol notation \(\boldsymbol{\overrightarrow{YE}}\) and \(\boldsymbol{\overrightarrow{YS}}\)).