Coordinates in the Plane

To represent points in the plane, two perpendicular straight lines are used. They are called the Cartesian axes or coordinate axes.

Cartesian Graph

The horizontal axis is called the x-axis.

The vertical axis is called the y-axis.

Point O, where the two axes intersect is called the origin.

The coordinates of a point, P, are represented by (x, y).

The distance measured along the horizontal axis is the x-coordinate or the abscissa.

The distance measured along the vertical axis is the y-coordinate or the ordinate.


Plotting Points

The coordinate axes divide the plane into four equal parts called quadrants.

Plotting Points

Signs

Quadrant Abscissa Ordinate
I + +
II +
III
IV +
Origin


The origin, O, has coordinates (0,0).

Vertical Axis


The points that are on the vertical axis have their abscissa equal to 0.

Horizontal Axis


The points that are on the horizontal axis have their ordinate equal to 0.

Ordinate


The points in the same horizontal line (parallel to the x-axis) have the same ordinate.

Abscissa


The points in the same vertical line (parallel to the y-axis) have the same abscissa.


Exercise

Plot the following points:

A(1, 4), B(-3, 2), C(0, 5), D(-4, -4), E(-5, 0), F(4, -3), G(4, 0), H(0, -2)

Cartesian Axis