Catesian system — lesson. Mathematics CBSE, Class 9.

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Number line:

3 (1).png

In the above number line, the position of point

$P$ in the above line can be represented as

$6$ units with reference to one line (horizontal line).

A similar rule applies to the negative side of the number line as well. It is possible to represent the position of a point with reference to more than one point.

Descartes invented placing two such number lines perpendicular to each other on a plane and locating points on the plane by referring them to these lines. The perpendicular lines may be in any direction. But, when we choose these two lines to locate a point in a plane in this chapter, one line will be horizontal(First image) and the other will be vertical(Second image), as below:

Let us combine these

$2$ lines in such a way they are perpendicular to each other. These two lines intersect each other at the point

$(0,0)$ .

Cartesian system:

It is a co-ordinate number system used to describe the position of a point in two dimensions by means of two perpendicular lines (x axis and y axis).

The line

$X'OX$ is the horizontal line called the

$x$ - axis.

The line

$Y'OY$ is the vertical line called the

$y$ - axis.

Co-ordinate axes:

The plural form of the axis is called the axes. A number line represented horizontally is the

$x$ - axis, and a number line represented vertically is the

$y$ - axis. Joining both the lines together at origin is called the

$xy$ plane or cartesian plane or co-ordinate axes.

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Signs in the graphs:

In

$x$ - axis, the point is positive along the direction

$OX$ and negative along the direction

$OX'$ .

In

$y$ - axis, the point is positive along the direction

$OY$ and negative along the direction

$OY'$ .

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