Determine the distance between each pair of points. Write...

Determine the distance between each pair of points. Write your answer in simplest radical form and then, when appropriate, approximate your answer to the nearest hundredth.
$$
(4,7) \text { and }(7,11)
$$

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Key Concepts

Distance Formula

The distance formula is a method derived from the Pythagorean theorem that calculates the straight-line distance between two points in the coordinate plane by taking the square root of the sum of the squares of the differences in their x and y coordinates.

Coordinate Geometry

Coordinate geometry, also known as analytic geometry, uses a coordinate system to describe and analyze the positions and relationships of points, lines, and shapes, allowing algebra to be used in solving geometric problems.

Simplest Radical Form

Simplest radical form involves expressing a square root in its most reduced form by extracting factors that are perfect squares, thus simplifying the radical without converting it to a decimal, which is useful for exact answers.

Approximation

Approximation refers to the process of finding a numerical value close to the exact value, often by rounding to a specified degree of accuracy, which is particularly useful when dealing with irrational numbers represented by radicals.

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