Math Problem Statement
Solution
The image shows a 3D cuboid along with the labeled axes , , and . 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 , and from the diagram:
- The -axis extends horizontally (left to right).
- The -axis extends horizontally (front to back).
- The -axis extends vertically (upward).
Let's analyze each point:
-
Point B:
- It lies on the -plane, meaning .
- , , so the coordinates of B are:
-
Point E:
- It lies directly above point A along the -axis.
- , , and , so the coordinates of E are:
-
Point F:
- This point shares the same -value as point C and the same -value as point E.
- , , and , so the coordinates of F are:
-
Point G:
- It lies at the farthest corner of the cuboid.
- , , and , so the coordinates of G are:
Final Coordinates:
Would you like more details about the coordinate system or the reasoning behind these points?
Here are 5 related questions to deepen your understanding:
- What are the coordinates of point A?
- What is the volume of this cuboid?
- How do we calculate distances between any two points in 3D space?
- What would the coordinates of point C be?
- 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
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