Q1. - Geometry

Question

For the following symbols, find the symbols that represent a line, segment, ray, or length.

 

a.  $\overline{PQ}$

b.  $\overrightarrow{PQ}$

c.  $\overleftrightarrow{PQ}$

d.  $PQ$

Step-by-Step Solution

Answer

a. The symbol $\overline{PQ}$ represents a segment.

b. The symbol $\overrightarrow{PQ}$ represents a ray.

c. The symbol $\overleftrightarrow{PQ}$ represents a line.

d. The symbol $PQ$ represents the length of the segment $\overline{PQ}$.

Part a. Step 1. Define the concept.

A segment is part of the line connecting two points. These two points are the endpoints of the segment.

Part a. Step 2. Find the symbol P Q ¯ that represents a line, segment, ray, or length.

The symbol $\overline{PQ}$ consists of two endpoints $P$ and $Q$, also all the points between $P$ and $Q$.

Since the symbol $\overline{PQ}$ has two endpoints, thus the symbol $\overline{PQ}$ represents a segment.

Part a. Step 3. Graphical interpretation of segment.

The following figure represents a segment $\overline{PQ}$.

Part b. Step 1. Define the concept.

A ray is a part of a line that has one endpoint and goes on infinitely in only one direction.

Part b. Step 2. Find the symbol P Q → that represents a line, segment, ray, or length.

The symbol $\overrightarrow{PQ}$ consists of one endpoint $P$ and $Q$ goes on infinitely.

 

Since the symbol $\overrightarrow{PQ}$ has one endpoint, thus the symbol $\overrightarrow{PQ}$  represents a ray.

Part b. Step 3. Graphical interpretation of ray.

The following figure represents a segment $\overrightarrow{PQ}$.

Part c. Step 1. Define the concept.

A line goes in the infinite direction on both sides, thus a line has no endpoints.

Part c. Step 2. Find the symbol P Q ↔ that represents a line, segment, ray, or length.

The symbol $\overleftrightarrow{PQ}$ consists of no endpoints.

 

Since the symbol $\overleftrightarrow{PQ}$ has no endpoints, thus the symbol $\overleftrightarrow{PQ}$  represents a ray

Part c. Step 3. Graphical interpretation of segment.

The following figure represents a line $\overleftrightarrow{PQ}$.

Part d. Step 1. Define the concept.

The length of a line segment can be measured by finding the distance between its two endpoints. It is the path between the two points with a definite length that can be measured.

Part d. Step 2. Find the symbol P Q that represents a line, segment, ray, or length.

Here the symbol $PQ$ represents the distance between the two endpoints $P$ and width="14" style="max-width: none; vertical-align: -4px;" $Q$ which is the length of the segment.

Part d. Step 3. Step description.

Thus, the symbol $PQ$ represents the length of the segment $\overline{PQ}$ .