What is the distance formula used to calculate the distance between two points (x₁, y₁) and (x₂, y₂)?

• A. √((x₂ - x₁) + (y₂ - y₁))
• B. √((x₂ - x₁)² + (y₂ - y₁)²)
• C. |x₂ - x₁| + |y₂ - y₁|
• D. (x₂ - x₁)² - (y₂ - y₁)²

Answer: (B)

The distance formula for calculating the distance between two points in a Cartesian coordinate system is derived from the Pythagorean theorem. When you have two points represented as (x₁, y₁) and (x₂, y₂), this formula enables you to find the straight-line distance between them.

In the context of the formula, (x₂ - x₁) represents the difference in the x-coordinates, and (y₂ - y₁) represents the difference in the y-coordinates. These differences form the two legs of a right triangle, where the distance between the points serves as the hypotenuse. According to the Pythagorean theorem, the length of the hypotenuse is found by taking the square root of the sum of the squares of the lengths of the legs.

Therefore, the correct distance formula is expressed as √((x₂ - x₁)² + (y₂ - y₁)²). This ensures that both the horizontal and vertical distances contribute to the total distance accurately, as squaring each difference accommodates the possibility of having negative values and calculates the lengths correctly.

As a result, the distance between the two points can be calculated effectively with this formula, providing both accuracy