Question

name the figure below in two different ways. (figure shows a line with points u, g, r, where u and r are endpoints and g is between them)

Explanation:

Step1: Identify the figure type

The figure is a line segment (has two endpoints \( R \) and \( U \), and a point \( G \) on it).

Step2: Name using endpoints

A line segment can be named by its two endpoints. So we can name it as Line segment \( RU \) (using \( R \) first then \( U \)) and Line segment \( UR \) (using \( U \) first then \( R \)). Also, since \( G \) is on the segment, we could name it as Line segment \( RG \) (from \( R \) to \( G \)) and Line segment \( GU \) (from \( G \) to \( U \)), but the most common two ways using the main endpoints are \( \overline{RU} \) and \( \overline{UR} \).

Answer:

1. Line segment \( RU \) (or \( UR \))
2. Line segment \( RG \) (or \( GR \)) and \( GU \) (or \( UG \)) is incorrect, the correct two ways are: Line segment \( RU \) (using the two endpoints \( R \) and \( U \)) and Line segment \( UR \) (also using the two endpoints \( U \) and \( R \)), or more accurately, since \( G \) is a point on the segment, we can also name it as Line segment \( RU \) (with endpoints \( R \) and \( U \)) and Line segment \( RGU \) is not standard. The standard two ways are: Line segment \( RU \) and Line segment \( UR \), or considering the point \( G \), we can say Line segment \( RU \) (with endpoints \( R \) and \( U \)) and Line segment \( RG \) (with endpoints \( R \) and \( G \)) but actually the main two ways for a line segment with endpoints \( R \) and \( U \) are \( \overline{RU} \) and \( \overline{UR} \). So the two ways are: Line segment \( RU \) and Line segment \( UR \) (or using the symbol \( \overline{RU} \) and \( \overline{UR} \)).