Page 213 - Maths Skills - 8

Introduction to Graphs 211

ORDERED PAIR
Any point in the Cartesian plane is located using the distance from the origin in specific order and is called an
ordered pair. For example to locate a point P (x, y), we first move from origin towards x-axis (left or right) and
then towards y-axis (up or down). Thus, P (x, y) is never same as P (y, x). The order has been fixed by convention
to standardise it.

COORDINATES OF A POINT
The position of a point in a plane is fixed with respect to its distance from the two coordinate axes. The perpendicular
distance from the y-axis is called the x-coordinate or abscissa of the point. The distance of the point from the
x-axis is called the y-coordinate or the ordinate of the point. Thus the coordinates of point P (a, b) are as marked
in the graph as below.

y-axis y-coordinate
Fact-o-meter
b P(a, b) The coordinates of origin
are always represented
Abscissa Ordinate by letter O (0, 0).

x-axis
O (0, 0) a
x-coordinate

Let’s Attempt

Example 1: Using the convention of signs, write the quadrant in which the following coordinates lie.
(i) (–3, 4) (ii) (5, 6) (iii) (7, –2) (iv) (–3, –7)

Solution: (i) (– 3, 4) since x-coordinate is negative and y-coordinate is positive, it lies in the II quadrant.
(ii) (5, 6) since both coordinates are positive, it lies in the I quadrant.

(iii) (7, – 2) since x-coordinate is positive and y-coordinate is negative, it lies in the IV quadrant.
(iv) (– 3, – 7) since both the coordinates are negative, it lies in the III quadrant.

Example 2: Write the coordinates of each of the points C, D, E, L and M as shown in the following figure.
Solution: Using ruler, draw perpendicular to the x-axis and
y-axis from each point C, D, E, L and M.
 C denotes (–2, –3) since distance of C from y-axis
is –2 units and from x-axis is –3 units.

 Similarly D denotes (4, – 4)
 E denotes (– 6, 2)
 L denotes (1, 3)

 M denotes (5, – 2)