gen-define-the-distance-formula-and-give-one-short-worked-exampl-fc80

Define the distance formula and give one short worked example.

# Distance Formula The **distance formula** calculates the straight-line distance between two points in a coordinate plane: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ where $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the two points. ## Worked Example Find the distance between points $A(1, 2)$ and $B(4, 6)$. **Solution:** $$d = \sqrt{(4 - 1)^2 + (6 - 2)^2}$$ $$d = \sqrt{(3)^2 + (4)^2}$$ $$d = \sqrt{9 + 16}$$ $$d = \sqrt{25} = 5$$ The distance between the points is **5 units**.