It is true that the distance formula is derived from the Pythagorean theorem.
The Pythagorean theorem states that:
Hypotenuse^2 = Opposite^2 + Adjacent^2
The distance formula is represented as:
[tex]xy = \sqrt{(x_2 -x_1)^2 + (y_2 - y_1)^2[/tex]
Take the square of both sides
[tex]xy^2 = (x_2 -x_1)^2 + (y_2 - y_1)^2[/tex]
By comparing both formulas, we have:
Hypotenuse = xy
Opposite = x2 -x1
Adjacent = y2 - y1
Hence, it is true that the distance formula is derived from the Pythagorean theorem.
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