Coordinate Geometry Notes

Two perpendicular number lines — the horizontal x-axis and the vertical y-axis — meet at a point called the origin, O. Together they form the Cartesian plane (coordinate plane). The axes divide the plane into four regions called quadrants, numbered I to IV anticlockwise starting from the upper right.

The position of any point is given by an ordered pair (x, y). The first number x is the x-coordinate or abscissa (distance from the y-axis, positive to the right). The second number y is the y-coordinate or ordinate (distance from the x-axis, positive upward).

Order matters: (3, 5) and (5, 3) are different points.

In Quadrant I both coordinates are positive (+, +). In Quadrant II, x is negative and y is positive (−, +). In Quadrant III both are negative (−, −). In Quadrant IV, x is positive and y is negative (+, −).

A point on the x-axis has y = 0, so it looks like (a, 0). A point on the y-axis has x = 0, so it looks like (0, b). The origin is (0, 0). Points lying on the axes are not counted in any quadrant.

So you can tell a point's quadrant just from the signs of its coordinates, without plotting it.

To plot (x, y): start at the origin, move x units along the x-axis (right if positive, left if negative), then move y units parallel to the y-axis (up if positive, down if negative), and mark the point.

To read the coordinates of a marked point, drop a perpendicular to the x-axis to get the abscissa and a perpendicular to the y-axis to get the ordinate.

Points with the same x-coordinate lie on a vertical line; points with the same y-coordinate lie on a horizontal line. For example, (2, 1), (2, 4), (2, −3) all lie on the vertical line x = 2.