Question

classify each figure as a line, ray, or line segment. then, show how to w (a) figure with points s, r, left arrow type: ∘ line ∘ ray ∘ line segment how to write it (b) figure with points o, p, two endpoints type: ∘ line ∘ ray ∘ line segment how to write it (c) figure with points t, u, arrows both ends type: ∘ line ∘ ray ∘ line segment how to write it

Explanation:

Part (a)

Step1: Identify the figure type

A ray has one endpoint and extends infinitely in one direction. The figure has endpoint \( R \) (wait, no, the arrow is from \( S \) to left, with \( S \) and \( R \) as points, but the arrow is on the left side from \( S \), so the endpoint is \( R \)? Wait, no: the figure has a point \( S \) with an arrow to the left, and \( R \) is a point. Wait, actually, a ray is named by its endpoint first, then another point on the ray. Wait, the figure: the line has a point \( R \) (no arrow) and \( S \) with an arrow to the left. So the endpoint is \( S \)? Wait, no, the arrow is on the left, so the ray starts at \( R \) (the point with no arrow) and goes through \( S \) to the left? Wait, no, the standard: a ray is a part of a line that starts at a point (endpoint) and extends infinitely in one direction. So if the figure has a point \( R \) (no arrow) and \( S \) with an arrow to the left, then the ray is \( \overrightarrow{RS} \)? Wait, no, the arrow is on the left, so the direction is from \( R \) through \( S \) to the left. So the type is ray.

Step2: Write the ray

A ray is written with the endpoint first, then another point on the ray, with an arrow over the endpoint and the other point. So the ray is \( \overrightarrow{RS} \) (wait, no, the arrow should be on the symbol. Wait, the correct notation: if the endpoint is \( R \) and it goes through \( S \) to the left, then it's \( \overrightarrow{RS} \)? Wait, no, the arrow direction: the ray starts at \( R \), goes through \( S \), so the notation is \( \overrightarrow{RS} \) (arrow from \( R \) to \( S \), but since it extends beyond \( S \), the arrow is over \( R \) and \( S \) with the arrow pointing in the direction of extension. Wait, maybe I got it wrong. Let's re-express: the figure has two points, \( R \) (no arrow) and \( S \) (with an arrow to the left). So the ray starts at \( R \), passes through \( S \), and extends infinitely to the left. So the type is ray, and it's written as \( \overrightarrow{RS} \) (the arrow is over \( R \) and \( S \), pointing towards the left, but in notation, we write the endpoint first, then the other point, with the arrow over them. So the type is ray, and the notation is \( \overrightarrow{RS} \).

Part (b)

Step1: Identify the figure type

A line segment has two endpoints and a definite length. The figure has two points \( O \) and \( P \), with no arrows, so it's a line segment.

Step2: Write the line segment

A line segment is written with the two endpoints, with a bar over them (no arrow). So it's \( \overline{OP} \).

Part (c)

Step1: Identify the figure type

A line extends infinitely in both directions. The figure has two points \( T \) and \( U \), with arrows on both ends, so it's a line.

Step2: Write the line

A line is written with the two points, with a double - headed arrow over them. So it's \( \overleftrightarrow{TU} \).

Answer:

s:
(a) Type: ray; How to write it: \( \overrightarrow{RS} \)
(b) Type: line segment; How to write it: \( \overline{OP} \)
(c) Type: line; How to write it: \( \overleftrightarrow{TU} \)