The distance from (0, 0) to (a, b) is

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The distance from (0, 0) to (a, b) is

The distance from the origin to a point (a, b) comes from the Pythagorean theorem. The horizontal change is a and the vertical change is b, so the distance squared equals a^2 + b^2. Taking the square root gives the distance: sqrt(a^2 + b^2). The signs of a and b don’t matter because they’re squared, and distance is nonnegative. The form with a^2 + b^2 under a square root is the correct distance, while the other expressions don’t match the geometric length of the vector (a, b); one is not even a distance in general, and another would be the squared distance without the square root.

The distance from the origin to a point (a, b) comes from the Pythagorean theorem. The horizontal change is a and the vertical change is b, so the distance squared equals a^2 + b^2. Taking the square root gives the distance: sqrt(a^2 + b^2). The signs of a and b don’t matter because they’re squared, and distance is nonnegative. The form with a^2 + b^2 under a square root is the correct distance, while the other expressions don’t match the geometric length of the vector (a, b); one is not even a distance in general, and another would be the squared distance without the square root.

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