# How do I find the distance between two points?

Jul 30, 2015

Use distance formula or Pythagorean Theorem

#### Explanation:

The formula is d=$\sqrt{{\left({x}_{1} - {x}_{2}\right)}^{2} + {\left({y}_{1} - {y}_{2}\right)}^{2}}$
if point A is (${x}_{1} , {y}_{1}$) and point B is (${x}_{2} , {y}_{2}$)

You can actually derive this from the Pythagorean Theorem. It's tough to show here, but set up a right triangle, connect Points A and B with a point C containing the right angle (${x}_{2} , {y}_{1}$). Then one leg will have length ${x}_{2} - {x}_{1}$ and the other leg will have length ${y}_{2} - {y}_{1}$. Using Pythagorean Theorem, you can take the sum of the lengths squared, take the square root, and that gives you the formula above.

Example: Points (2, -3) and (-1, 5)

$d = \sqrt{{\left(2 - \left(- 1\right)\right)}^{2} + {\left(- 3 - 5\right)}^{2}}$
=$\sqrt{{\left(3\right)}^{2} + {\left(- 8\right)}^{2}}$
=$\sqrt{9 + 64} = \sqrt{73}$