California Assessment of Student Performance and Progress (CAASPP) Math Practice Exam

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

1. d = √((x₂ - x₁)² + (y₂ - y₁)²)

2. d = √((y₂ - y₁)² + (x₂ - x₁)²)

3. d = (x₂ - x₁) + (y₂ - y₁)

4. d = |x₂ - x₁| + |y₂ - y₁|

The correct answer is: d = √((x₂ - x₁)² + (y₂ - y₁)²)

The distance formula between two points \((x₁, y₁)\) and \((x₂, y₂)\) is based on the Pythagorean theorem, which describes the relationship between the lengths of the sides of a right triangle. When calculating the distance between two points in a Cartesian coordinate system, you can think of the horizontal and vertical changes as forming the two legs of a right triangle. The formula \(d = \sqrt{(x₂ - x₁)² + (y₂ - y₁)²}\) effectively calculates the length of the hypotenuse of this triangle. The expression \((x₂ - x₁)²\) represents the square of the horizontal distance between the two points, while \((y₂ - y₁)²\) represents the square of the vertical distance. By squaring these distances, adding them, and then taking the square root, you obtain the straight-line distance between the two points. This method of calculating distance is crucial in various fields such as geometry, physics, and computer science, where understanding the spatial relationship between points is essential. The other options do not correctly express the distance between two points in the Cartesian plane. The second option