coordinate geometry

What is Coordinate Geometry?

A system that uses coordinates to represent points, lines, and shapes in a two-dimensional plane.

How do you calculate the distance between two points?

Using the formula: $d = \sqrt{(x<em>2 - x</em>1)^2 + (y<em>2 - y</em>1)^2}$, where $(x<em>1, y</em>1)$ and $(x<em>2, y</em>2)$ are the coordinates of the two points.

How do you find the midpoint of a line segment?

Using the formula: $M = (\frac{x<em>1 + x</em>2}{2}, \frac{y<em>1 + y</em>2}{2})$, where $(x<em>1, y</em>1)$ and $(x<em>2, y</em>2)$ are the coordinates of the endpoints of the line segment.

How do you calculate the slope of a line?

The slope $m$ is calculated as: $m = \frac{y<em>2 - y</em>1}{x<em>2 - x</em>1}$, where $(x<em>1, y</em>1)$ and $(x<em>2, y</em>2)$ are two points on the line.