Which scenario best illustrates the use of the Pythagorean theorem?

The Pythagorean theorem is a fundamental principle in geometry that applies specifically to right triangles. It states that in a right 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. One of the primary applications of this theorem is to calculate distances in a two-dimensional space, which is exactly what the selected scenario covers.

When determining the distance between two points, say (x1, y1) and (x2, y2) in a Cartesian coordinate system, you can imagine a right triangle formed by these points. The horizontal leg of the triangle runs along the x-axis and the vertical leg along the y-axis. By applying the Pythagorean theorem to this triangle, you can derive the distance formula:

Distance = √[(x2 - x1)² + (y2 - y1)²].

This clearly illustrates how the Pythagorean theorem is used in practical scenarios involving coordinates and distance calculations.