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).```plaintext2. 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 DiagramThe 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,

In the coordinate space there are 3 axes. These are the x, y, z axes. All the 3 axes are…

Answered: 2. Determine the coordinates of each…

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 (

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.1: Systems Of Equations

Problem 61E

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Concept explainers

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A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.

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,

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