# GRE Algebra | Coordinate Geometry

In the **coordinate geometry**, all the points are located on the coordinate plane. Coordinate plane is also called xy-plane.

**The concepts of xy-plane are:**

- The horizontal number line is called the x-axis and vertical number line is called the y-axis.
- The intersection point of both the axes is called the origin, denoted by O.
- The positive half of the x-axis right of the origin and negative half of x-axis is left to the origin.
- The positive half of the y-axis is above the origin and negative half of y-axis is below the origin.
- Two axes divide the plane into four Quadrants I, II, III and IV starting.

In **xy-plane** every point is denoted by P(x, y). Here first number is called the x-coordinate and second number is called the y-coordinate. A point having coordinates (3, 2) is located 3 units to the right of y-axis and 2 units above to the x-axis as shown in the above plane.

**Distance between two points:-**

In xy-plane the distance between the two points (x_{1}, y_{1}) and (x_{2}, y_{2}) can be found by using the **Pythagoras theorem**.

**Example:** Find the distance between the points (2, 3) and (-1, -1).

**Explanation:**

Distance between two points can be calculated using the below formula:

Distance = √ [ (x_{2}- x_{1})^{2}+ (y_{2}- y_{1})^{2}) ]

Put all the values,

Distance = √[ (-1 - 2)^{2}+ (-1 - 3)^{2}) ] = √[ (-3)^{2}+ (-4)^{2}) ] = √[ 9 + 16 ] = √25 = 5

Hence, distance between these two points is **5 unit**.