2. Determine the coordinates of each point. H has been given to you. point A ( point D ( E point H ( 6, 10, 7 ) point G ( point C ( point B ( B. point F ( 10 point E (

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
icon
Related questions
icon
Concept explainers
Question
Please help me determine the coordinates of each point
### Coordinate Geometry: Determining Points in a 3D Space

**Objective:**
- Determine the coordinates of each point in a given 3-dimensional space. Point H has been provided.

**Provided Information:**
- Point H has coordinates (6, 10, 7).

```plaintext
2. Determine the coordinates of each point. H has been given to you.

point A (       ,       ,       )     point D (       ,       ,       )

point H ( 6 , 10 , 7 )                  point G (       ,       ,       )

point C (       ,       ,       )     point B (       ,       ,       )

point E (       ,       ,       )     point F (       ,       ,       )  
```

### Explanation of the Diagram

The diagram represents a rectangular prism in a 3-dimensional coordinate space with the following points labeled:

- Points A, B, C, and D form the base.
- Points E, F, G, and H form the top.
- The coordinates along the x-axis range from 0 to 10.
- The coordinates along the y-axis are not explicitly given beyond point H's y-coordinate of 10.
- The z-coordinate is 7 at the level of the top plane where points E, F, G, and H lie.

Assuming that opposite edges of the prism are equal in length and all angles are 90 degrees, we can infer the coordinates of the other points based on the information provided for point H:

### Steps to Determine the Coordinates:

1. **Point H (6, 10, 7)** is already given.

2. **Point G** is directly beneath point H, with the same x and y coordinates, but z-coordinate as 0 since it lies on the x-y plane.
   - Point G (6, 10, 0)

3. **Point F** is directly above point G, along the z-axis.
   - Point F (6, 0, 7)

4. **Point E** is directly below point F.
   - Point E (6, 0, 0)

5. **Point B** is aligned with point E and point C on the z-plane.
   - Point B (0, 10, 0)

6. **Point A** is directly beneath point H on the x-y plane.
   - Point A (0, 10,
Transcribed Image Text:### Coordinate Geometry: Determining Points in a 3D Space **Objective:** - Determine the coordinates of each point in a given 3-dimensional space. Point H has been provided. **Provided Information:** - Point H has coordinates (6, 10, 7). ```plaintext 2. Determine the coordinates of each point. H has been given to you. point A ( , , ) point D ( , , ) point H ( 6 , 10 , 7 ) point G ( , , ) point C ( , , ) point B ( , , ) point E ( , , ) point F ( , , ) ``` ### Explanation of the Diagram The diagram represents a rectangular prism in a 3-dimensional coordinate space with the following points labeled: - Points A, B, C, and D form the base. - Points E, F, G, and H form the top. - The coordinates along the x-axis range from 0 to 10. - The coordinates along the y-axis are not explicitly given beyond point H's y-coordinate of 10. - The z-coordinate is 7 at the level of the top plane where points E, F, G, and H lie. Assuming that opposite edges of the prism are equal in length and all angles are 90 degrees, we can infer the coordinates of the other points based on the information provided for point H: ### Steps to Determine the Coordinates: 1. **Point H (6, 10, 7)** is already given. 2. **Point G** is directly beneath point H, with the same x and y coordinates, but z-coordinate as 0 since it lies on the x-y plane. - Point G (6, 10, 0) 3. **Point F** is directly above point G, along the z-axis. - Point F (6, 0, 7) 4. **Point E** is directly below point F. - Point E (6, 0, 0) 5. **Point B** is aligned with point E and point C on the z-plane. - Point B (0, 10, 0) 6. **Point A** is directly beneath point H on the x-y plane. - Point A (0, 10,
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Points, Lines and Planes
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning