2. CO-ORDINATE GEOMETRY
In this chapter we shall first define the coordinates
of a point in a plane with reference to two
mutually perpendicular lines in the same plane.
We shall also learn about the plotting of points of
points on the plane (Cartesian plane) which will be
used to draw the graphs of linear equations in
one/two variables in the Cartesian plane.

4. HOW TO PLOT POINTS ON THE GRAPH?
 Take a graph paper.
 Draw two mutually perpendicular lines on the graph paper, one
horizontal and other vertical.
 Might their intersection point as O (origin). The horizontal line
as X’OX and the vertical line as Y’OY. The line X’OX is the x-
axis and the line Y’OY as the y-axis.
 Choose a suitable scale on x-axis and y-axis and mark the points
on both the axis.
 Obtain the coordinates of the point which is to be plotted. Let
the point be P (a,b). To plot this point, start from the origin
and move’│a│’ units along OX and OX’ according as ‘a’ is
positive or negative. Suppose we arrive at point M. from point
M move vertically upward or downward through │b │ units
according as b is positive or negative. The point where we arrive
finally is the required point P(a,b).

5. PLOTTING A POINT ON THE GRAPH(3,4)
P
(3,4)
THUS POINT P REPRESENTS (3,4) ON THE GRAPH

6. PLOTTING A POING ON THE GRAPH (-4,2)
N (-4,2)
THUS POINT N REPRESENTS (-4,2) ON THE GRAPH

7. PLOTTING A POINT ON THE GRAPH (-2,-5)
X
(-2,-5)
THUS POINT X REPRESENTS (-2,-5) ON THE GRAPH

8. PLOTTING A POINT ON THE GRAPH (2,-4)
(2,-4)
Z
THUS POINT Z REPRESENTS (2,-4) ON THE GRAPH

9. SUMMARY
• In order to locate the position of a point in a
plane we require two perpendicular lines. One of
them is horizontal and another is vertical. The
plane is called the Cartesian plane and the lines
are known as the coordinate axes. The horizontal
line is called the x-axis and the vertical line is
known as the y-axis.
• The coordinates axes divide the plane into four
parts which are known as quadrants.
• The point of intersection of the coordinate axes is
called the origin.
• The coordinates of the origin are (0,0)

10. • The distance of a point from x-axis is called its x-
coordinate, or abscissa and the distance of the
point from y-axis is called its y-coordinate or
ordinate.
• If x and y denote respectively the abscissa and
ordinate of a point P, then (x,y) are called the
coordinates of point P.
• The y-coordinate of every point on y-axis is zero.
So, the coordinates of any point on x-axis are of
the form (x,0).
• The x-coordinate of every point on x-axis is zero.
So, the coordinates of any point on y-axis are of
the form (0,y)

11. • The signs of coordinate (x,y)of a point in
various quadrants are as given below –
QUADRANT COORDINATES
X y
1 + +
2 - +
3 - -
4 + -