### Theory:

The great scientist and mathematician Sir Isaac Newton once quoted the following:

"Geometry is that a part of universal mechanics which accurately proposes and demonstrates the art of measuring".

In \(1637\), Rane Descartes, an eminent philosopher and mathematician gave a new idea, that is "The geometric shapes and structures can be delivered algebraically using the coordinates of the points which make up the shapes".

To describe the position of a point with respect to one line like in the case of a number line is easier. But there are some situations in which we might need to describe the position of a point with respect to more than one line.

We can learn this with an example:

Describe the position of a table lamp in your room table from your side.

It can be like, consider the lamp as a point and table as a plane. Choose the two perpendicular edges of the table from your side.

Measure the distance of the lamp from the longer edge, suppose it is \(25\) \(cm\). Again, measure the length of the lamp from the shorter edge, and suppose it is \(15\) \(cm\). You can write the position of the lamp as \(15cm\), \(25cm\) or \(25cm\), \(15cm\), depending on the order you fix.

Measure the distance of the lamp from the longer edge, suppose it is \(25\) \(cm\). Again, measure the length of the lamp from the shorter edge, and suppose it is \(15\) \(cm\). You can write the position of the lamp as \(15cm\), \(25cm\) or \(25cm\), \(15cm\), depending on the order you fix.

In the discussion above, you observe that position of any object lying in a plane can be represented with the help of two perpendicular lines.

In the case of 'dot', we require a distance of the dot from the bottom line as well as from the left edge of the paper.

Let's take a look at another scenario:

There is a main road running in the North-South direction and streets with numbering from west to east. Also, on each street, house numbers are marked. To locate your friend's house in this place from where you started is one point of reference enough?

That is if we know she is living in the street \(2\),

This is how the location of a point (that is \(C\) in the figure) with reference to two lines helps to make the real-life process easier.

Similarly, if we want to find the position of \(M\) in the above figure, it should be house number \(4\), \(7th\) street.

**can we find her house**?**Yes**, but it would be not easy to trace. Instead, if we know she is living in the street \(2\) house number \(5\), it would be easy to trace.This is how the location of a point (that is \(C\) in the figure) with reference to two lines helps to make the real-life process easier.

Similarly, if we want to find the position of \(M\) in the above figure, it should be house number \(4\), \(7th\) street.

**This simple idea has far-reaching consequences and has given rise to a significant branch of Mathematics known as Coordinate Geometry**.