Coordinate Geometry — Formula Sheet

The x-coordinate (abscissa) is the distance of a point from the y-axis.

The y-coordinate (ordinate) is the distance of a point from the x-axis.

Coordinates of a point on the x-axis: (x, 0)

Coordinates of a point on the y-axis: (0, y)

PQ = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

PQ = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}

OP = \sqrt{x^2 + y^2}

For points (3, 2), (-2, -3), and (2, 3), the distances are PQ = √50, QR = √52, and PR = √2.

These points form a right triangle because PQ² + PR² = QR².

For points (7, 1) and (3, 5), the relation between x and y for an equidistant point is x - y = 2.

Distance from the origin uses OP = √(x² + y²).

For two points P(x1, y1) and Q(x2, y2), the distance is PQ = √((x2 - x1)² + (y2 - y1)²).