Answer:
√37 ≈ 6.083
Explanation:
You want the distance between the points (2, -1) and (3, 5).
Distance formula
The distance formula can be used.
d = √((x2 -x1)² +(y2 -y1)²)
d = √((3 -2)² +(5 -(-1))²) = √(1 +36)
d = √37 ≈ 6.083 . . . . units
The distance between the two points is √37, about 6.083 units.
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Additional comment
The distance formula makes use of the Pythagorean theorem. It treats the difference of x-coordinates and the difference of y-coordinates as legs of the right triangle with the distance of interest being the hypotenuse.
In vector terms, the segment between the two points can be considered a vector extending from one point to the other. The length is the "norm" of the vector, the root of the sum of the squares of its components.
A calculator can perform the same computation by finding the absolute value (modulus) of the complex number (2 -i) -(3 +5i) = (-1 -6i). |-1 -6i| = √37.
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