Lab Manual: Find the Values of Abscissae | Lab Manuals for Class 9 PDF Download

Objective

Materials Required
Cardboard, White paper, Graph paper with various given points, Geometry box, Scissors, Glue

Prerequisite Knowledge
(i) Knowledge of cartesian coordinate system.
(ii) To locate/plot a point in cartesian plane.

Theory

The point of intersection of these lines is called origin and it is denoted by O. In other words, the point from which distances are marked is called origin. The horizontal line XOX’ is called  X-axis and the vertical line YOY’ is called Y-axis. Directions OX Fig. 16.1

and OY are called the positive directions of X-axis and Y-axis, respectively and directions OX’ and OY’ are called the negative directions of X-axis and Y-axis, respectively.

Note:

• The angle between the horizontal and vertical axes is 90°.
• Any line perpendicular to the X-axis is parallel to the Y-axis.
• ny line perpendicular to the Y-axis is parallel to the X-axis.

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.
x-coordinate and y-coordinate taken together are called cartesian coordinates or coordinates of a point and denoted by (x, y). Here, the x-coordinate comes first and after this y-coordinate comes. (x, y) is called an order pair.
The order of x and y is important in (x, y). Position of (y, x) will be different from (x, y).

Procedure

• Take a cardboard of suitable size and paste a white paper on it.
• Now, paste the graph paper with various points drawn on it in the’ middle of white paper.
• Now, look at the graph paper and the points whose abscissae and ordinates are to be found.

Demonstration
If P is a point plotted on graph paper and we have to find the abscissa and ordinate of point P.
Draw perpendiculars PM and PN from P to X-axis and Y-axis, respectively.
PN = -2 units (distance from X-axis, i.e. x-coordinate or abscissa)
PM = 9 units (distance from Y-axis, i.e. y-coordinate or ordinate)
6As, point P lies in second quadrant.
So, the coordinates of P are (- 2,9).

Note:
Care should be taken while reading the coordinates, otherwise the location of the object will differ.

Observation

Fill the above table for different points on the given graph.

Result
The coordinates of the points plotted on the graph paper have been found.

Application
This activity is very useful in locating the position of a particular country/city or a place on map.