Algebra Practice Test

The distance between two points in a two-dimensional Cartesian coordinate system, represented by the points (x1, y1) and (x2, y2), is calculated using the distance formula derived from the Pythagorean theorem. This formula is C: Distance = √[(x2 - x1)² + (y2 - y1)²].

To understand why this formula is correct, consider that the difference in the x-coordinates (x2 - x1) and the difference in the y-coordinates (y2 - y1) represent the lengths of the legs of a right triangle formed by these two points. The distance between the points is the length of the hypotenuse of this triangle.

According to the Pythagorean theorem, the square of the length of the hypotenuse (the distance we are trying to find) is equal to the sum of the squares of the other two sides. Therefore, we square the differences in each coordinate: (x2 - x1)² and (y2 - y1)². Finally, we take the square root of the sum of these squares to find the actual distance.

This understanding reinforces why the correct answer is based on the underlying geometric principles,