Cartesian plane is a two dimensional co-ordinate system. This system has two axis – the x-axis and the y-axis. The center of the Cartesian plane is called the origin.

The x-axis and the y-axis divide the plane into 4 different quadrants as shown in the figure above. The axis are real number line with 0 at the origin.

Any point on the plane is plotted in terms of horizontal distance on x-axis and vertical distance on y-axis.

where is distance on x-axis and is distance on y-axis.

Example: Plot a point for

Solution:

If then

## Pythagorean Theorem and Distance Formula

Pythagorean theorem is used for finding the distance of hypotenuse of a right triangle. The formula is modified to find the distance of two point on the Cartesian plane.

The above triangle has three sides – a, b and c, then Pythagorean theorem is given by

Suppose there are two points on the Cartesian plane.

p (x1, y1) = (2, 4) q (x2, y2) = (2, 2)

and we have to find the distance between them.

Using Pythagorean theorem, we get

a = | y2 – y1 | = length of a

b = | x2 – x1 | = length of b

Therefore,

Distance formula for two points is

The above diagram verify the results and it shows that the distance is actually 2 units. Hence, the distance formula is correct and applies to the Cartesian plane.