# Slope of a plane

## Main Question or Discussion Point

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

rachmaninoff
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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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.

HallsofIvy