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# Drop a perpendicular to line

benpaulthurston shared this question 5 years ago

I don't know the vocab to describe the type of math that geogabra lets you do on points, where multiplication is like a dot product and you can make a formula that applies to all the coordinates, if someone could let me know that would be nice. Here I found a way to do what they call in geometry "dropping a perpendicular" to a line where I defined the line as a parameterization with a variable from point A to point Z. I've proven it for the 2d case though the formula really looks like it would work in any number of dimensions. Anyway, thanks if someone could point me on what to google to see what theorems in this kind of math have been proven, as I'm sure this one I've found is thanks!

Here is a good way I found to use geogabra's point types to make a circle...

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maybe I don't know enough about geogabra and it can do this somehow but it would be interesting to define circles like this using geogabras basic point types, the equation at the bottom (P-C)^2=4 should be true when P is 2 unit lengths away from C, so the locus would be a circle. so if there were a variable point type maybe? I'm not sure.

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Here is a good way I found to use geogabra's point types to make a circle...

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Here is a good way I found to use geogabra's point types to make a circle...

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Maybe you are looking for a command as following

1. proveNum = Q ≟ ClosestPoint[Line[A, Z], P] <- Returns true || false

.

Or maybe you are looking for something like here in Prove[].

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no maybe it was confusing with the example i proved about the perpendicular, my question is what type of geometry or algebra is this that im doing in this program, some keyword so i can research more about it, specifically that you can write formulas that work on points no matter how many dimensions the points have, its the same formula over all the components, i figure there has to be some word or phrase for that type of formula, thx