Distance Formula Math Example 1

Solution

1. 1
   The distance formula is derived from the Pythagorean theorem: the horizontal and vertical separations form the legs of a right triangle, and the distance is the hypotenuse. $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.
2. 2
   Identify the coordinates: $(x_1, y_1) = (1, 2)$ and $(x_2, y_2) = (4, 6)$. Compute the differences: $x_2 - x_1 = 3$, $y_2 - y_1 = 4$.
3. 3
   Substitute: $d = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$. Recognise the 3-4-5 Pythagorean triple — no calculator needed.