Page 34 - Mathematics Class - IX

Unit 3 Coordinate geometryte geometry
Coordina

ACTIVITY 3.1

OBJECTIVE
To find the values of abscissae and ordinates of various points given in a Cartesian plane.

MATERIALS REQUIRED

Cardboard Geometry box
White paper Pencil
Graph paper with various given points

PRE-REQUISITE KNOWLEDGE

1. Knowledge of Cartesian coordinate system.
2. Knowledge of plotting of points in the Cartesian plane.

THEORY
1. Cartesian coordinate system: The system used to describe the position of a point in a plane is called
Cartesian coordinate system.

In Cartesian system, there are two perpendicular directed straight lines XX′ and YY′ which intersect at point
O. The line XX′ will be horizontal line and YY′ will be vertical line. The point of intersection of these lines
is called origin and it is denoted by O.
2. Coordinates of a point in Cartesian plane: To locate a point in the Cartesian plane, its perpendicular
distances from X-axis and Y-axis are required, these distances are called coordinates of the point. Each
point in Cartesian plane has two coordinates; X-coordinate and Y-coordinate.
(i) The X-coordinate of a point is the perpendicular distance from the Y-axis measured along the X-axis
(positive, along the positive direction of the X-axis and negative, along the negative direction of X-axis).
The X-coordinate is also called the abscissa.
(ii) The Y-coordinate of a point is the perpendicular distance from the X-axis measured along the Y-axis
(positive, along the positive direction of the Y-axis and negative, along the negative direction of Y-axis).
The Y-coordinate is also called the ordinate.

PROCEDURE

1. Take the cardboard and paste a white paper on it.
2. Paste the given graph paper along with various points drawn on it as shown in Fig. (a).

3. Look at the graph paper and the points whose abscissae and ordinates are to be found.
4. To find abscissa and ordinate of a point, say A, draw perpendiculars AM and AN from A to X-axis
and Y-axis, respectively. Then abscissa of A is OM and ordinate of A is ON. Here, AN = OM = 2 and
AM = ON = 9. The point A is in first quadrant. Coordinates of A are (2, 9).

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