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 Apr 26 comment If a 3D-cake is cut by $n$ planes yielding the maximum number of pieces, then what is the number of pieces with the cake crust? @joriki edited the question Apr 26 revised If a 3D-cake is cut by $n$ planes yielding the maximum number of pieces, then what is the number of pieces with the cake crust? added 53 characters in body Mar 5 asked Transform and domain such that phase shift of the original function results in shift in transformed domain variable Mar 4 awarded Popular Question Nov 10 awarded Revival Nov 4 comment Why can't a triangular matrix with only zeros in its diagonal be invertible? Laplace expansion can yield that such matrix determinant is zero, thus it's uninvertible. en.wikipedia.org/wiki/Laplace_expansion Aug 27 answered How to trace the path of a moving point in geogebra Aug 20 asked Compute phase-shifted variant of a real-valued function Dec 16 revised Finding closest point perpendicular to B 1/2 is not needed Dec 16 comment Finding closest point perpendicular to B Dec 16 revised Finding closest point perpendicular to B missed 1/2 Dec 16 comment Finding closest point perpendicular to B However, changing $B$ to $B=(4,8)$ looks right. Try to substitute all the points for this new $B$. Dec 16 comment Finding closest point perpendicular to B Your specified $D=(7,5)$ doesn't satisfy your original problem, because $CD$ isn't parallel to $AB$. Your $D$ is not the correct $D$. Dec 16 comment Finding closest point perpendicular to B You mean that your calculated value $(8,49)$ differs from pre-defined known answer? Would you provide the example script that leads you to that? Dec 10 comment Finding closest point perpendicular to B Solution of the system of two equations above is the formula which expresses $dx$ and $dy$ directly from known coordinates of points $A, B, C$. Solving two-variable systems of simple equations is quite a typical homework for teens. This Q&A site discourages direct answers for homework questions but encourages answers that lead to questioner's own efforts. As you may have already noticed, there are way too few people who would bother stuffing your numbers into the system and yielding you an exact formula on a silver plate. Try doing something and ask further questions if any. Dec 9 comment Finding closest point perpendicular to B @SinanSamet I've updated the answer to reflect the idea more basically Dec 9 revised Finding closest point perpendicular to B expanded modulus Dec 8 comment Finding closest point perpendicular to B From there on you've got two equiations for two variables, $dx$ and $dy$. Solve them to get the desired $D=(dx,dy)$. Dec 4 comment Finding closest point perpendicular to B Rewrite $|CD|$ via it's coordinates using $|Z|=\sqrt {Zx^2+Zy^2}$. The second one is fine - there are actually two points $D$ that satisfy the conditions, one of them to the left of $AB$, another - to the right. Dec 3 answered Finding closest point perpendicular to B