Question

name the figure below in two different ways. symbol: → □ and

Explanation:

Step1: Identify the figure type

The figure is a ray, which has a starting point and extends infinitely in one direction. The starting point here can be considered as \( P \) or \( G \) or \( C \), but typically we use the endpoint first.

Step2: Name using endpoint and another point

One way is to use the endpoint \( P \) and another point on the ray, say \( C \), so it can be named \( \overrightarrow{PC} \). Another way is to use the endpoint \( P \) and point \( G \), so it can be named \( \overrightarrow{PG} \). Also, since a ray can be named by its endpoint and any other point on it, another common way is to recognize that the ray starts at \( P \) and goes through \( G \) and \( C \), so it can be named \( \overrightarrow{PC} \) (using \( P \) as the endpoint and \( C \) as a point on the ray) and also, if we consider the direction, it can be named with the endpoint first, so another way is \( \overrightarrow{PG} \) (using \( P \) as endpoint and \( G \) as a point on the ray). Wait, actually, the ray has an endpoint at \( P \) (since the arrow is going away from \( P \) towards \( C \)? Wait no, the arrow is at \( C \), so the ray starts at \( P \) and extends through \( G \) and \( C \), so the endpoint is \( P \), and it goes through \( G \) and \( C \). So the two ways to name the ray are: 1. Using the endpoint \( P \) and a point on the ray, say \( G \): \( \overrightarrow{PG} \) 2. Using the endpoint \( P \) and a point on the ray, say \( C \): \( \overrightarrow{PC} \)

Wait, maybe I got the direction wrong. Let's check the diagram: the ray has a point \( P \) at the top, then \( G \), then \( C \), with the arrow at \( C \). So the ray starts at \( P \) and goes towards \( C \), so the endpoint is \( P \), and it passes through \( G \) and \( C \). So the two names can be \( \overrightarrow{PG} \) (since \( G \) is on the ray from \( P \)) and \( \overrightarrow{PC} \) (since \( C \) is on the ray from \( P \)). Alternatively, sometimes rays are named by their endpoint and the direction, but in standard notation, a ray is named with its endpoint first, followed by another point on the ray. So the two ways are \( \overrightarrow{PC} \) and \( \overrightarrow{PG} \), or maybe \( \overrightarrow{PG} \) and \( \overrightarrow{PC} \). Wait, actually, the ray can be named as \( \overrightarrow{PC} \) (with endpoint \( P \), going through \( C \)) and also, since \( G \) is between \( P \) and \( C \), it can be named as \( \overrightarrow{PG} \) (with endpoint \( P \), going through \( G \)).

Answer:

\(\overrightarrow{PC}\) and \(\overrightarrow{PG}\) (or other valid combinations where the first point is the endpoint \( P \) and the second is a point on the ray, like \( \overrightarrow{PG} \) and \( \overrightarrow{PC} \))