https://file.aiquickdraw.com/mathbot/file/1729645644636gu1d3ksq.jpg

The image shows a 3D cuboid along with the labeled axes \(x\), \(y\), and \(z\). The vertices of the cuboid are labeled, and you are asked to identify the coordinates of points B, E, F, and G.

The origin point is \( O \), and from the diagram:
- The \(x\)-axis extends horizontally (left to right).
- The \(y\)-axis extends horizontally (front to back).
- The \(z\)-axis extends vertically (upward).

### Let's analyze each point:

- **Point B**:
  - It lies on the \(xy\)-plane, meaning \(z = 0\).
  - \(x = 3\), \(y = 4\), so the coordinates of B are:
    \[
    B(3, 4, 0)
    \]

- **Point E**:
  - It lies directly above point A along the \(z\)-axis.
  - \(x = 3\), \(y = 0\), and \(z = 12\), so the coordinates of E are:
    \[
    E(3, 0, 12)
    \]

- **Point F**:
  - This point shares the same \(y\)-value as point C and the same \(z\)-value as point E.
  - \(x = 3\), \(y = 4\), and \(z = 12\), so the coordinates of F are:
    \[
    F(3, 4, 12)
    \]

- **Point G**:
  - It lies at the farthest corner of the cuboid.
  - \(x = 0\), \(y = 4\), and \(z = 12\), so the coordinates of G are:
    \[
    G(0, 4, 12)
    \]

### Final Coordinates:
- \( B(3, 4, 0) \)
- \( E(3, 0, 12) \)
- \( F(3, 4, 12) \)
- \( G(0, 4, 12) \)

Would you like more details about the coordinate system or the reasoning behind these points?

Here are 5 related questions to deepen your understanding:
1. What are the coordinates of point A?
2. What is the volume of this cuboid?
3. How do we calculate distances between any two points in 3D space?
4. What would the coordinates of point C be?
5. Can you identify a diagonal in the cuboid and calculate its length?

**Tip**: In 3D geometry, always check which plane a point lies on by identifying any axis with a zero coordinate.

Look at the cuboid below, and check the position of x, y, and z axis. Please identify the coordinate of B, E, F, G.

Learn how to identify coordinates of specific points in a 3D cuboid based on the x, y, and z axes. This problem teaches the basics of 3D geometry and coordinate systems, suitable for students in Grades 9-12.

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