Math Problem Statement
Solution
The question is asking to determine the distance from point to the midpoint of edge of a cube, where the edge length is cm.
Understanding the Diagram
- The cube has vertices labeled .
- is the topmost corner of the cube (opposite vertex ).
- is one of the edges on the base of the cube.
Approach:
-
Coordinates of Key Points:
- Assuming the cube is aligned along the axes:
- Assuming the cube is aligned along the axes:
-
Midpoint of :
- The midpoint of can be found using the midpoint formula:
-
Distance between and :
- The distance formula in 3D is:
- Substituting the coordinates of and :
Thus, the distance from to the midpoint of is .
The correct answer is option c: cm.
Would you like further details on any part of the solution?
Related Questions:
- How do you find the distance between two points in 3D space?
- What is the formula to find the midpoint of a line segment?
- How do you generalize the distance formula for higher dimensions?
- Can this problem be solved using vectors instead of coordinates?
- What are the practical applications of distance formulas in geometry?
Tip: Always ensure to apply the correct formula when dealing with 3D coordinates, considering all three axes for accurate results.
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Math Problem Analysis
Mathematical Concepts
3D Geometry
Distance Formula
Midpoint
Formulas
Distance formula: d = √((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)
Midpoint formula: M = ((x1 + x2)/2, (y1 + y2)/2, (z1 + z2)/2)
Theorems
Pythagoras theorem in 3D
Suitable Grade Level
Grades 9-11
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