The coordinates on a map for San Francisco are (53,17) and...

The coordinates on a map for San Francisco are $(53,17)$ and those for Sacramento are $(123,78)$ . Note that coordinates represent miles. Find the distance between the cities to the nearest mile.

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Key Concepts

Rounding

Rounding is the process of adjusting a numerical value to a specified degree of precision, often to simplify the number for practical use. This concept is important when the calculated distance needs to be presented in a more understandable, whole-number format, such as to the nearest mile.

Pythagorean Theorem

The Pythagorean theorem is a key principle in geometry that relates the three sides of a right triangle by stating that the square of the hypotenuse is equal to the sum of the squares of the other two sides. This theorem underlies the derivation of the distance formula used in coordinate geometry.

Distance Formula

The distance formula provides a method to calculate the straight-line (Euclidean) distance between two points in a coordinate plane. It is derived from the Pythagorean theorem and involves taking the square root of the sum of the square of differences between corresponding coordinates.

Coordinate System

A coordinate system is a framework for determining the position of points using numerical values, typically arranged in perpendicular axes. This system is fundamental in mapping and spatial analysis, where positions are specified as coordinates in a plane.

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