AFOQT Practice Test

What is the distance between two points represented by the formula d = √[( x₂ - x₁)² + (y₂ - y₁)²]?

1. The straight line connecting the two points

2. The average of the two points

3. The midpoint of the two points

4. The difference in altitude between the two points

The correct answer is: The straight line connecting the two points

The correct interpretation of the formula \( d = \sqrt{(x₂ - x₁)² + (y₂ - y₁)²} \) is that it calculates the straight-line distance between two points in a Cartesian coordinate system, based on their coordinates \((x₁, y₁)\) and \((x₂, y₂)\). This formula is derived from the Pythagorean theorem, where the differences in the x-coordinates and the y-coordinates represent the lengths of the two legs of a right triangle, and the distance \(d\) represents the hypotenuse. The other options do not accurately describe the distance between two points: the average of the two points would suggest a mean value rather than a distance, the midpoint refers to the point that is equidistant from both points, and the difference in altitude solely pertains to vertical measurement without considering horizontal displacement. Thus, the statement that the distance is the straight line connecting the two points is correct.