How do you find the distance between two points (1, 2) and (4, 6)?

To determine the distance between two points (1, 2) and (4, 6) in a Cartesian plane, the correct formula to use is derived from the Pythagorean theorem. The distance formula is given by:

Distance = √((x₂ - x₁)² + (y₂ - y₁)²)

In this case, the coordinates are (x₁, y₁) = (1, 2) and (x₂, y₂) = (4, 6). Plugging these values into the distance formula yields:

Distance = √((4 - 1)² + (6 - 2)²)

By calculating the differences, we see that (4 - 1) equals 3 and (6 - 2) equals 4. Thus, the computation becomes:

Distance = √(3² + 4²) = √(9 + 16) = √25 = 5.

This reveals that the calculation of the distance accurately reflects the geometric relationship between the two points, capturing both horizontal and vertical distances in a single formula. The square root operation ensures that the result is a non-negative value.

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