1. Coordinate Plane 2. Distance Formula 3. How does the distance formula show the Pythagorean Theorem?
The distance formula is derived from the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In the coordinate plane, the distance formula calculates the distance between two points using their coordinates. The formula is:
√((x2 - x1)² + (y2 - y1)²)
This formula resembles the Pythagorean theorem when applied to a right-angled triangle. By finding the difference between the x-coordinates and y-coordinates of the two points, squaring these differences, and summing them, we are essentially finding the squared lengths of the two shorter sides of a right-angled triangle. Taking the square root of this sum gives us the length of the hypotenuse, which is equivalent to the distance between the two points on the coordinate plane.Therefore, the distance formula essentially demonstrates the Pythagorean theorem in the context of the coordinate plane.