Coordinate Geometry

Coordinate geometry (analytic geometry) studies geometric figures by representing them with algebraic equations using coordinates. The plane is described by ordered pairs (x, y), and geometric objects like lines and circles can be written as equations involving x and y.

Important properties

• The distance between two points (x1, y1) and (x2, y2) is given by the distance formula: $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

• The midpoint of the segment joining (x1, y1) and (x2, y2) is $\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$

• The equation of a line can be written as $y = mx + c$, where m is the slope and c is the y-intercept.

• The slope of a line through (x1, y1) and (x2, y2) is $m = \frac{y_2 - y_1}{x_2 - x_1}$