Use coordinates, distance, and algebra to prove or disprove simple geometric statements.
Complete a missing coordinate calculation in a proof step
Problem
Complete the missing coordinate calculation in this proof step: Distance from \(A\)\((1,2)\) to \(B\)\((4,6)\) is \(\text{\_\_\_}\).
Big Picture
What this problem is really about
First identify what kind of quantity the proof blank requests, because slope, displacement, and distance use the same coordinate changes differently. For distance, treat the horizontal and vertical changes as perpendicular legs, square and add them, and take the nonnegative square root so the result is one scalar length.
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