# Slope of a plane

laminatedevildoll
Suppose that there's a flat 3-d plane with points A,B,C,D. The midpoint is X. How do I find the equations for each of the points if the plane is slightly warped (meaning, that its sort slightly of bent). If I were to find the slopes on each side of the plane, would it matter that it's slightly warped?

Thnx

## Answers and Replies

What do you mean by 'warped'? If it's not flat then it's not a mathematical plane, and using plane formulas will give you at best approximations.

The general equation for planes is ax + by + cz = d; if it's not a purely vertical plane then you can express z as a function of x and y, z(x , y) = ux + vy + w, with u = - a/c, v = - b/c, w = d/c.

edit: A question, are you talking about an infinite (unbounded) plane, or a quadrilateral with corners A,B,C,D?

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laminatedevildoll
rachmaninoff said:
What do you mean by 'warped'? If it's not flat then it's not a mathematical plane, and using plane formulas will give you at best approximations.

The general equation for planes is ax + by + cz = d; if it's not a purely vertical plane then you can express z as a function of x and y, z(x , y) = ux + vy + w, with u = - a/c, v = - b/c, w = d/c.

edit: A question, are you talking about an infinite (unbounded) plane, or a quadrilateral with corners A,B,C,D?

Just a 3d rectangular shaped object with sides A,B,C,D. Warped meaning that when you take a rectangular piece of paper and if you slightly bent the sides at the long ends of the paper, one corner will be higher than its opposite side, up and down.