Theory:

Geometry is that a part of universal mechanics that accurately proposes and demonstrates the art of measuring.
- Sir Isaac Newton.
Did you know how the concept of coordinate geometry came into existence?
Rane Descartes.jpg
 
Rene Descartes is a famous French mathematician.
 
One day Rene became quite ill. While he was taking rest in his bed, he noticed an insect flying around the ceiling and sits at various places on the ceiling. He wanted to know all the places where the insect sits. So, he draws horizontal and vertical lines in the paper, which indicates the ceiling.
 
1259_2.png
 
These points mark the places where the insect sits on the ceiling. He plotted the points using directions and the insect's movement in the north, south, east and west directions. Then, later he called the place \((x,y)\), where \(x\) indicates the horizontal direction (east and west direction) and \(y\) indicates the vertical direction (north and south direction). This is how coordinate geometry came into existence.
In \(1637\) Rane Descartes published a book called "la geometric", in his book he gave a new idea that is each point is expressed by an ordered pair of algebraic real numbers \((x, y)\) are called coordinates.
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 coffee cup in your room table with reference to another person. It can be like,
 
1 (1).png
 
Consider the coffee cup as a point and the table as a plane. Choose any two perpendicular edges of the table.
 
Measure the distance of the lamp from the longer edge, say it is \(30 \ cm\). Again, measure the distance of the lamp from the shorter edge, and suppose it is 15 cm. You can write the position of the lamp as \((15, 30)\) or \((30, 15)\), 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.
 
This simple idea has far-reaching consequences,and has given rise to a very important branch of Mathematics known as Coordinate Geometry.
Reference:
https://en.wikipedia.org/wiki/Ren%C3%A9_Descartes#/media/File:Frans_Hals_-_Portret_van_Ren%C3%A9_Descartes.jpg
Frans Hals drew the portrait of Rene Descartes.