Rectangular coordinate system

The position of a point in a plane is determined by two coordinates. The method is as follows:

Two mutually perpendicular lines (straight lines) XX' and YY' are drawn as shown in the figure.

These straight lines are termed as coordinate axes, the one (usually drawn horizontally) is called the x-axis or the axis of abscissa (XX' is the x-axis) and the other is the y-axis or the axis of ordinate (YY' is the y-axis). The point O, the intersection of the two axes is called the origin of the coordinates.

It is customary to choose the positive direction as in figure, so that a counter clockwise rotation of the ray OX through 90⁰ will bring it to coincidence, with positive ray OY.

The coordinate axes XX', YY' (with established positive direction and an appropriate scale unit) form a rectangular co-ordinate system.

Rectangular co - ordinates

The position of the point P in a plane in the rectangular co-ordinate system is determined as follows:

Draw PA and PB perpendicular to XX' and YY'.

The segment OA = a measures the distance along the x-axis (the x-coordinate and the perpendicular distance AP = OB = b ( parallel to y - axis) measures the y-coordinate. The coordinates of P are (a, b).

These numbers may be positive or negative depending on the direction of OA and OB. The number 'a' is called the abscissa of the point and the number 'b' is called the ordinate of the point.

In the figure, the point P has abscissa x = 2, and the ordinate y = 3 (scale unit is 1cm = 1 unit). This information is usually written as P (2,3). Generally, the notation P (a, b) means that the point P has abscissa x = a and the ordinate y = b.

Examples:

1) If a point A is (-2, 3), then its abscissa is -2 and ordinate is 3.

2) If a point B is (-4, -5), then its abscissa is -4 and ordinate is -5.

3) If a point S is (4, 2) then its abscissa is 4 and ordinate is 2.