Find the exact distance between the two points. Where...

Find the exact distance between the two points. Where appropriate, also give approximate results to the nearest hundredth.
$$
\left(-\frac{1}{3}, \frac{2}{3}\right),\left(\frac{1}{3},-\frac{4}{3}\right)
$$

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Key Concepts

Exact vs Approximate Values

In many mathematical problems, it is important to distinguish between exact answers, which may be expressed in terms of fractions or radicals, and approximate values, which are numerical estimates rounded to a certain level of precision. This distinction allows for precise computations and more practical numerical interpretations where needed.

Distance Formula

The distance formula is a method used in coordinate geometry to calculate the distance between two points in the plane. It is derived from the Pythagorean theorem, and it involves taking the square root of the sum of the squares of the differences between corresponding coordinates.

Pythagorean Theorem

The Pythagorean theorem is a fundamental principle in Euclidean geometry that relates the sides of a right triangle. It states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides, which underpins the derivation of the distance formula in the coordinate plane.

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