Get the corner position of a diagonal line

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Hello,

I imagine this is a super simple math issue and my brain has just turned to mush but how would I go about getting the corner/ intersection point of 2 points that are at an angle from each other. Please see the attached image for an example.

Thanks

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This question contains several ambiguities that should be taken into account:
- if you define the corner point as "equidistant" from the 2 provided points, you get infinite points on the bisecting plane of the line.
- if you define the corner point as "right angle" you get infinite points on a sphere (which the line is the diameter of)

However, if both of these definitions are adhered to, you still get infinite valid points on a circle. More information is needed to get a unique solution.

If the context of the problem is to find a corner on the 3D bounding box of this line, you can pick and choose xyz components of each endpoint and combine them.
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it's pretty simple:
you take your line and mark its middle point.
from there it's the same distance to the unknown point as to one of the known ones (length a).
So you get your unknown point by going tangentially starting at the middle point by length a.

Cheers
CYTE
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