Sports A soccer player passes the ball from a point that is...

Sports A soccer player passes the ball from a point
that is 18 yards from the endline and 12 yards from the
sideline. A teammate who is 42 yards from the same
endline and 50 yards from the same sideline receives
the pass. (See figure.) How long is the pass?

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Key Concepts

Coordinate Geometry

Coordinate geometry involves representing points in a plane using numerical coordinates and using algebraic equations to model geometric relationships. This concept allows the setting up of a coordinate system to describe positions and distances in real-life scenarios, such as determining positions on a sports field.

Distance Formula

The distance formula is used to calculate the straight-line distance between two points in a plane. Derived from the Pythagorean theorem, it provides a precise method of finding the distance by taking the square root of the sum of the squares of the differences of the coordinates.

Pythagorean Theorem

The Pythagorean theorem is a fundamental principle in geometry that relates the sides of a right triangle. It states that the square of the hypotenuse is equal to the sum of the squares of the other two sides, which is the basis for the distance formula used in calculating distances in coordinate geometry.

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