<p>How can I improve my 3d visualization skills, enough so that I can solve SAT problems involving cubes and rectangular prisms correctly...? Like the ones that ask me to find the distance between two points on a cube. Help?</p>
<p>I'm fine with the basic ones, like the ones that ask to find the surface areas and volumes of figures, but I need help with the stuff I mentioned above?</p>
<p>Yes. I am a bad artist who can't draw anything beyond stick figures.</p>
<p>Perhaps you can try not having to visualize them?</p>
<p>The formula for two points on a cube is simply sqrt((delta x)^2 + (delta y)^2 + (delta z)^2)</p>
<p>Delta variable is defined as the change in that variable, for example the x of the first point minus the x of the second point. Order doesn’t matter because m - n = -(n-m), and since you square it (-w)^2 = (w)^2.</p>
<p>Sorry if I’m not much help.</p>
<p>Finding the distance between two points on a cube (and more generally a rectangular solid) falls into 2 categories:</p>
<p>(a) if the 2 points are on the same face of the rectangular solid you will probably use the Pythagorean Theorem</p>
<p>(b) otherwise it is probably a “long diagonal” problem. In this case you can use the “Generalized Pythagorean Theorem”: d^2 = l^2 +w^2 + h^2. Here l, w and h are the length, width and height, respectively.</p>