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Coordinates of a Point

Let P be any point in the Cartesian plane. From P, draw PM perpendicular to X′OX. Then,
(i) the distance from y-axis (OM) is called x-coordinate or abscissa of P and is usually denoted
by x.

(ii) the distance from x-axis (PM) is called y-coordinate or ordinate of P and is usually denoted
by y.
(iii) x and y taken together are called coordinates of P. It is written in the form of an ordered
pair as (x, y) or P(x, y).

Thus, corresponding to a point P in the 4 Y Tells how many units
Cartesian plane, we get an ordered pair to move towards
(x, y) of integers. Here abscissa = x and 3 the right.
ordinate = y. P(x, y) or (3, 2)
2
For example, the coordinates of P are Tells how many
units to move
(3, 2) as abscissa is 3 and ordinate is 2. 1 Ordinate y upward.
Remember that (3, 2) and (2, 3) are two M
different points. X′ –4 –3 –2 –1 O 1 Abscissa 3 4 X
2
We observe that, –1 x

• The coordinates of the origin are (0, 0). –2
• For any point on x-axis, its ordinate is –3
zero. So, the coordinates of any point
on x-axis are like (x, 0). Thus, each –4
of the points (8, 0), (–9, 0) lies on the Y′
x-axis.
• For any point on y-axis, its abscissa is zero. So, the coordinates of any point on y-axis are like
(0, y). Thus, each of the points (0, 8), (0, –9) lies on the y-axis.

Quadrants and Sign Convention

The two axes X′OX and YOY′ divide the plane into four parts called quadrants, where

(i) XOY is called first quadrant.
Here, both x-coordinate and y-coordinate are Y
positive.
Second First
(ii) X′OY is called second quadrant. Quadrant Quadrant
(–, +) (+, +)
Here x-coordinate is negative and y-coordinate is
positive.

(iii) X′OY′ is called third quadrant. X′ O X
Here both x-coordinate and y-coordinate are
negative. Third Fourth
Quadrant Quadrant
(iv) Y′OX is called fourth quadrant. (–, –) (+, –)
Here x-coordinate is positive and y-coordinate is
negative. Y′

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