INTRODUCTION TO COORDINATE GEOMETRY

Often the integers are shown as specially-marked points evenly spaced on the line. The line includes all real numbers, continuing forever in each direction.

figure  S.1

The left side of zero consists of negative integers and the right side of zero consists of positive integers.

Zero is not marked as positive or Negative. therefore zero is neither positive nor negative.

The number line can be constructed horizontally as the above number line and vertically as shown below:

figure  S.2

Note that, constructing vertically, positive integers must be above zero and negative integers must be below zero. it is like rotating horizontal number line anticlockwise 90° about the origin (0). The following flash video clip will give you a good picture:

figure  S.3

When joining vertical and horizontal number line we get something called Cartesian plane or XY plane as shown above.

Cartesian plane or xy plane has two lines vertical and horizontal axis, the horizontal axis is called x-axis and vertical axis is called y-axis.

Points in Cartesian plane are plotted according to their vertical and horizontal position. Consider point A in the figure below:

figure  S.4

Travelling along horizontal axis from origin i.e. 0 to reach point A, we travel 3 units, while travelling along vertical axis from origin i.e. 0 to reach point A, we travel 4 units.

From that explanation we say:

The x – coordinate of A is +3

The y – coordinate of A is +4

Therefore we say that, the coordinates of point A are (3,4) or A is the point (3,4), the x-coordinate is given first then the y-coordinate.

Now from above figure  S.4 the coordinate of the other points are:

B (-4, 1),  C(4,1),  D(-2,-1),  E(0,2) and F(2,0)

NOTE: the place where the two axes intersect is called the Origin and the point of origin is (0,0)

Try your understanding:

1 .  Sketch your own axes and plot the following points:

       A(3, -1), B(-2, -3), C(-1,4),  D(0,0), E(0,-4) and F(4, 2).

2. Study the following Coordinate plane  and answer the questions

1. Write down the coordinates of the points M, T, P, Y and Q
2. What is the vertical distance from Point G to point Q? Click
3. What is the horizontal distance from point Y to point M?

3. Connect the points A(0,1),  B(4,1),  C(5,-2), D(-2,-2) on XY Plane
     and state the shape you obtain.

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