3 Vocabulary Terms - Define/Illustrate
1. Coordinate Plane 2. Distance Formula 3. How does the distance formula show the Pythagorean Theorem?
1. Coordinate Plane: A coordinate plane is a two-dimensional plane formed by a horizontal line called the x-axis and a vertical line called the y-axis. The point where the two axes intersect is called the origin, denoted as (0,0). Points on the coordinate plane are represented by ordered pairs (x,y), where x is the distance from the y-axis and y is the distance from the x-axis.
2. Distance Formula: The distance formula is a mathematical formula used to calculate the distance between two points in a coordinate plane. It is derived from the Pythagorean theorem and is given by d = √((x2-x1)² + (y2-y1)²), where (x1, y1) and (x2, y2) are the coordinates of the two points and d is the distance between them.
3. The distance formula shows the Pythagorean theorem because it is derived from it. In a right triangle, the distance between two points (x1, y1) and (x2, y2) can be calculated as the hypotenuse of a right triangle with legs of lengths (x2-x1) and (y2-y1). By applying the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two other sides, we arrive at the distance formula. This formula is essentially a generalized form of the Pythagorean theorem applied to any two points in a coordinate plane.