Coordinate System and Graphs

# Coordinate System and Graphs

## Coordinate System and Graphs

Coordinate System

On a graph paper, draw two lines XOX’ and YOY’ mutually perpendicular to each other intersecting at O.

1. The horizontal line XOX’ is called X-axis.
2. The vertical line YOY’ is called Y-axis.
3. XOX’ and YOY’ together are called              coordinate axes.
4. The point of intersection of XOX’ and YOY’, i.e., O is called the origin.

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

The two axes divide the plane into four parts each of which is called a quadrant. Quadrants are named I, II, III and IV in anti-clockwise direction. This representation of axis, quadrants, etc., is called coodinate plane or XY plane and the axis are called coordinate axes.

The sign of the coordinates are given below:

1.      In first quadrant, x is positive, y is positive.
2.      In second quadrant, x is negative, y is positive.
3.      In third quadrant, x is negative, y is negative.
4.      In fourth quadrant, x is positive, y is negative.

## Coordinates of a Point

Let P be a point on the coordinate plane. Draw AP perpendicular to X-axis and BP perpendicular to Y-axis then

BP is called the x-coordinate or abscissa of point P and is denoted by x.
AP is called the y-coordinate or ordinate of point P and is denoted by y.
The abscissa and the ordinate of a point are called the coordinates of point P and is represented as an ordered pair (x, y).

Coordinates of the origin is (0, 0), coordinates of any point on X-axis is (x, 0) and on Y-axis is (0, y). Thus, the coordinate of a point specify the position of a point with reference to the coordinate axes.

## Plotting of Points

For plotting points on the graph paper, follow the given steps.

1. Draw XOX’ and YOY’.
2. Choose a scale on both the axes and label it.
3. To plot a point, B (4, –3) move 4 units along x-axis towards right of zero and then move 3 units along the direction of negative y-axis and mark the point B.
The coordinates of point B are (4, –3).

Example 1: Plot the following points on a graph paper and state the quadrant on which they lie.
A (5, 3), B (–3, 2), C (7, 7), D (–4, –5), E (6, –2), F (0, 5), G (–6, 0)

Solution: On a graph paper, draw coordinates XOX’ and YOY’ intersecting each other at O. The given points are plotted on the graph paper as shown. The quadrants on which the given points lie are
A (5, 3) — 1st quadrant
B (–3, 2) — 2nd quadrant
C (7, 7) — 1st quadrant
D (–4, –5) — 3rd quadrant
E (6, –2) — 4th quadrant
F (0, 5) — y-axis
G (–6, 0) — x-axis

## Graphs of Linear Equations

In order to draw the graph of a linear equation, proceed as shown.
1. In the given equation, give some value to one variable and find the corresponding value of the other variable. Express these values in a tabular form.
2. Plot these points and join any two points by a straight line. To determine a straight line only two points are required but it is suggested that three coordinates are determined.

Example 2: Draw the graph of each of the following.
5x – 4y = 15
Solution: The given equation is 5x – 4y = 15, i.e., x = (15 + 4y)/5 .
The table for the solution of the equation is given as:

 x 3 7 -1 y 0 5 -5

Plot the points A (3, 0), B (7, 5), C (–1, –5) to get the graph of the equation.

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