The coordinates of a point

​ ​This is Maria's house, and this is her friend, Mikhail's house. Their houses are marked at different places on a map. To find the way from Maria's house to Mikhail's, you first go right and then upwards on the map. Mikhail's house lies two steps to the right and three steps up from Maria's. If we add numbers to the lines on this map, we get two number lines; one horizontal and one vertical.

We give these number lines names: X and Y. The horizontal is X and the vertical is Y. We call them the X-axis and the Y-axis. Maria's house lies where the axes cross. This place is called the origin.

At the origin, both the X and Y axes have zero values. Mikhail's house lies where X is 2 and Y is 3. ​ ​We describe a position on the map by giving its co-ordinance. The map itself then becomes a coordinate system. The coordinates of a point tell us how far along the X-axis and how high up the Y-axis it lies. We write coordinates of a point like this: first a letter, and then two numbers in parentheses.

The first number is the X coordinate and the second one is the Y coordinate. Let's call the place where Maria's house stands, M sub 0, and X and Y coordinates for this point are 0 and 0. And let's call Mikhail's house M sub 1. The coordinates for M sub 1 are 2 and 3. The X coordinate always comes before the Y coordinate. ​ ​This is Maria's grandma's house.

As you can see, her grandma lives on the other side of the Y-axis. Just like on a number scale, the X and Y axes can also have negative values. Grandma's house lies at the point M sub 2. The coordinates are -4 on the X-axis and 2 on the Y-axis. As always, we write the X coordinate first.

The closest store to Maria's house lies at to the point M sub 3, whose coordinates are -3 and -1. To find the store's position, we first have to find the right spots on both axes. The X coordinate for M sub 3 is -3. A negative X coordinate means that we go left on the X-axis. The Y coordinate for M sub 3 is -1.

A negative Y coordinate means that we go down. We now have the values on both axes and we know where the store is. ​ ​Maria's school is at M sub 4, which has an X coordinate of 2 and a Y coordinate of -3. A positive X coordinate means that we go to the right, 1, 2, and a negative Y coordinate means that we go down. You can see that Mikhail's house, grandma's house, a store, and the school, are in different regions. These regions are called quadrants.

Mikhail lives in the first quadrant. And then we go counter-clockwise. Grandma lives in the second quadrant, the store is in the third quadrant, and the school is in the fourth quadrant. ​ ​The X and Y axes together represent a coordinate system. Just like a sheet of paper or any flat figure, it has two dimensions: length and width. The X and Y axes make a two dimensional plain.

A point's position on the plane can be described by two numbers. The first one is the X coordinate, and the second one is the Y coordinate. A positive value means that you go to the right from the origin along the X-axis and up along the Y-axis. A negative value means you go left on the X-axis and down on the Y-axis. X and Y axes cross at zero, or the origin.

This is where Maria's house is. The person who first thought of this system was a 17th century philosopher and mathematician called Rene Descartes, or Cartesias in Latin. This system is called Cartesian coordinate system after him.