A Cartesian coordinate system is a two-dimensional plane defined by an x-axis (horizontal) and a y-axis (vertical), used to graphically represent algebraic equations. Each point in the plane is identified by an ordered pair of coordinates $(x, y)$.
Quadrant: One of four sections into which a Cartesian plane is divided by its axes.
Distance Formula: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ calculates the distance between two points in a Cartesian plane.
Midpoint Formula: $M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$ finds the midpoint between two points on a Cartesian plane.