1996 AHSME Problems/Problem 28
Problem
On a rectangular parallelepiped, vertices , , and are adjacent to vertex . The perpendicular distance from to the plane containing , , and is closest to
Solution
By placing the cube in a coordinate system such that is at the origin, , , and , we find that the equation of plane is:
The equation for the distance of a point to a plane is given by:
Note that the capital letters are coefficients, while the lower case is the point itself.
Thus, the distance from the origin (where ) to the plane is given by:
Since , this number should be just a little over , and the correct answer is .
Note that the equation above for the distance from a point to a plane is a 3D analogue of the 2D case of the distance formula, where you take the distance from a point to a plane. In the 2D case, both and are set equal to .
See also
1996 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 27 |
Followed by Problem 29 | |
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