Math Problem Statement

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

Solution

The image shows a 3D cuboid along with the labeled axes xx, yy, and zz. 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 OO, and from the diagram:

  • The xx-axis extends horizontally (left to right).
  • The yy-axis extends horizontally (front to back).
  • The zz-axis extends vertically (upward).

Let's analyze each point:

  • Point B:

    • It lies on the xyxy-plane, meaning z=0z = 0.
    • x=3x = 3, y=4y = 4, so the coordinates of B are: B(3,4,0)B(3, 4, 0)
  • Point E:

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

    • This point shares the same yy-value as point C and the same zz-value as point E.
    • x=3x = 3, y=4y = 4, and z=12z = 12, so the coordinates of F are: F(3,4,12)F(3, 4, 12)
  • Point G:

    • It lies at the farthest corner of the cuboid.
    • x=0x = 0, y=4y = 4, and z=12z = 12, so the coordinates of G are: G(0,4,12)G(0, 4, 12)

Final Coordinates:

  • B(3,4,0)B(3, 4, 0)
  • E(3,0,12)E(3, 0, 12)
  • F(3,4,12)F(3, 4, 12)
  • G(0,4,12)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.

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Math Problem Analysis

Mathematical Concepts

3D Geometry
Coordinate Systems
Cuboids

Formulas

Coordinate points in 3D space (x, y, z)

Theorems

Basic geometry in three-dimensional space

Suitable Grade Level

Grades 9-12