What do you think of this explanation for why perpendicualar lines have negative reciprocal slope?

What do you think of this explanation for why perpendicualar lines have negative reciprocal slope?
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Answer :

I think it has potential, but I think as of now you’re taking it on faith that the lines are perpendicular. I understand your explanation about fixing them in place, but it is not proven that the x and y axes would lie through A and B when rotated. It wouldn’t be hard to add that bit on, I think.
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