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(c) Mark point C at a distance of 4 units to the left of origin.

(d) Mark point D at a distance of 2 units to the right of origin.

Origin
C B D A
–5 –4 –3 –2 –1 0 1 2 3 4 5

Location of a Point

We saw that the number line can be used to locate the position of a point. However, in some
situations, a single reference number is not sufficient to locate a point. For example, when you

go to watch a movie and to locate your reserved seat, you need to know two numbers, the row
number and the seat number.

Similarly, to locate the exact location or position of a point in a plane, we need two number lines
that are perpendicular to each other.

Coordinate Axes and Cartesian Plane

Draw two number lines X′OX and YOY′ perpendicular to each other (horizontal and vertical) at
point O on a graph paper. Then,

(a) the point O is called the origin.
(b) the horizontal line X′OX is called the x-axis.

(c) the vertical line YOY′ is called the y-axis.

(d) X′OX and YOY′ taken together are called coordinate axes.

The plane containing both the coordinate axes is called the Cartesian plane.

Y
4
y-axis
3
Knowledge Desk
2

Origin x-axis The Cartesian plane was introduced
1
by French mathematician Rene
Descartes (1596-1650) after he
X′ –4 –3 –2 –1 O 1 2 3 4 X noticed a fly on the ceiling while
–1 lying in bed. He determined that the
fly’s position could be characterised
–2 by its left and right positions as well Rene Descartes
as its up and down positions. (1596–1650)
–3 To characterise the position of the fly, he created
the xy coordinate system, which is now referred
–4
to as the Cartesian plane.
Y′

315 Introduction to Graphs