Two artifacts are found at a dig. If a coordinate plane is...

Two artifacts are found at a dig. If a coordinate plane is set up, one artifact was found at $(1,5)$ and the other artifact was found at $(3,1)$ How far apart were the two artifacts? Round to the nearest tenth. (lesson 9.5 )

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Key Concepts

Rounding

Rounding involves approximating a numerical value to a specified degree of precision. In many practical problems, after calculating an exact value, one rounds the result—such as to the nearest tenth—to simplify the answer or match required specifications.

Pythagorean Theorem

The Pythagorean theorem is a fundamental relation in Euclidean geometry that relates the lengths of the sides of a right triangle. It is the principle underlying the distance formula, explaining how the squares of the horizontal and vertical distances add up to the square of the direct distance between two points.

Distance Formula

The distance formula is used to calculate the distance between two points on a coordinate plane. It is derived from the Pythagorean theorem and involves finding the differences in the x-coordinates and y-coordinates, squaring these differences, summing them up, and then taking the square root of the result.

Coordinate Geometry

Coordinate geometry deals with points, lines, and figures plotted on a coordinate plane. It allows one to use algebraic methods to solve geometric problems, such as finding the distance between two artifacts or other points given their coordinates.

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