AFOQT Practice Test

When calculating the distance using the distance formula, what does (x₂ - x₁)² + (y₂ - y₁)² represent?

1. The total vertical distance

2. The square of the horizontal and vertical differences

3. The actual path distance traveled

4. The average distance of points

The correct answer is: The square of the horizontal and vertical differences

The representation of (x₂ - x₁)² + (y₂ - y₁)² in the distance formula indeed refers to the square of the horizontal and vertical differences. In the context of finding the distance between two points in a Cartesian coordinate system, (x₂ - x₁) calculates the difference in the x-coordinates (horizontal difference), while (y₂ - y₁) calculates the difference in the y-coordinates (vertical difference). By squaring both differences, you emphasize their contributions to the total distance and comply with the Pythagorean theorem, which is fundamental in determining the direct distance between those points. This squared sum is then square-rooted to yield the straight-line distance, but its critical part lies in correctly calculating and summing the squared differences of both dimensions, establishing a foundational aspect of Euclidean geometry.