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Why do you square the values in the Pythagorean Theorem or any distance formula wherein you're trying to find the distance between two points in two-dimensional, Euclidean space?

for example, why are we squaring the difference in the two $x,x$ values and two $y,y$ values?

$a^2 = b^2 + c^2$

Jennifer Melfi
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  • you think of this by considering the proof of Pythagoras theorem by taking squares on the sides of the triangle and if you can find the combination you can apply this to the distance formula –  Apr 30 '15 at 05:42

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This GIF (jiff) is very instructive.

enter image description here

louie mcconnell
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