Which is the correct formula to find the distance between two points A(B) and C(D)?

The correct formula to find the distance between two points A(x₁, y₁) and B(x₂, y₂) in a 2D Cartesian coordinate system is:

D = √((x₂ – x₁)² + (y₂ – y₁)²)

Here’s how the formula works:

• Subtract the x-coordinates of the two points to find the horizontal distance: (x₂ – x₁).
• Subtract the y-coordinates to find the vertical distance: (y₂ – y₁).
• Square both results: ((x₂ – x₁)² and (y₂ – y₁)²).
• Add these squared values together.
• Finally, take the square root of the total to get the Euclidean distance between the two points.

This formula is derived from the Pythagorean theorem, which relates the lengths of the sides of a right triangle to its hypotenuse. In this case, the distances along the x and y axes form the two shorter sides of the triangle, while the distance D is the hypotenuse.