Final answer:
The equation d(u, v) = √(v₁ - u₁)² + (v₂ - u₂)² is the distance formula for calculating the Euclidean distance between two points in a two-dimensional space.
Step-by-step explanation:
The given equation is the formula for calculating the Euclidean distance between two points in a two-dimensional space. It is often referred to as the distance formula.
Let's break down the formula:
d(u, v): The distance between point u and point v
v₁, u₁: The x-coordinates of points v and u, respectively
v₂, u₂: The y-coordinates of points v and u, respectively
To prove the equation, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
By applying the Pythagorean theorem to the difference between the x-coordinates and the y-coordinates of points v and u, we can derive the formula d(u, v) = √((v₁ - u₁)² + (v₂ - u₂)²).