# 2D Coordinate Geometry - Problem Solving

###### This wiki is incomplete.

PS: Here are examples of great wiki pages — Fractions, Chain Rule, and Vieta Root Jumping

This page has examples for problem-solving techniques that primarily involve 2D coordinate geometry.

## Examples

The most fundamental formula applied in 2D coordinate geometry is the distance formula

\[ \begin{eqnarray} \text{(Distance travelled)} &=& \sqrt{ (\text{rise})^2 +(\text{run})^2} \\ &=& \sqrt{ (\Delta x)^2 + (\Delta y)^2}. \end{eqnarray} \]

If I walk 15 kilometers north and then another 36 kilometers west, what is the displacement?

By the Pythagorean theorem, I have traveled \(\sqrt{15^2 + 36^2} = 39 \) kilometers. \(_\square \)

**Cite as:**2D Coordinate Geometry - Problem Solving.

*Brilliant.org*. Retrieved from https://brilliant.org/wiki/2d-coordinate-geometry-problem-solving/