Distance Between Two Points

In Figure 1.1.6, P(x₁ y₁) and Q(x₂, y₂) are two different points in the (x, y) plane. As we move from P to Q, the coordinates x and y will change by amounts that we denote by Δx and Δy. Thus

change in x = Δx = x₂ - x₁,

change in y = Δy = y₂ - y₁

Figure 1.1.6

The quantities Δx and Δy may be positive, negative, or zero. For example, when x₂ > x₁, Δx is positive, and when x₂ < x₁, Δx is negative. Using Δx and Δy we define the basic notion of distance.

One can also get this formula from the Theorem of Pythagoras in geometry: The square of the hypotenuse of a right triangle is the sum of the squares of the sides.