We are learning the basics of Data Science. This is the second article on **Coordinate Geometry** which is the second step of the data science foundation. Read the first article on Linear Algebra basics here.

## Introduction to Coordinate Geometry

The study of geometry with coordinate points is known as **Coordinate Geometry**. It describes the link between geometry and algebra through graphs to solve geometric problems. Coordinate geometry is also known as **Cartesian Geometry**.

In coordinate geometry, the position of points on the plane is described using an ordered pair of numbers called** coordinates**. To locate the position of a point or to find the coordinates of a point on a plane, we require a pair of **coordinate axes (the x-axis and y-axis)**. The distance of a point from the y-axis is called its **x-coordinate, or abscissa**. A point’s x-coordinate, also known as its abscissa, is its distance from the y-axis. Y-coordinate, also known as ordinate, is a point’s distance from the x-axis. Points on the x- and y-axes have coordinates of the forms (x, 0) and (0, y), respectively.

In coordinate planes, we have two axes labeled as the x-axis** (horizontal axis)** and **y-axis (vertical axis)**, which are perpendicular to each other. The points at which these axes intersect are called the origin (0, 0). Coordinates are two variables (x, y) that indicate a point’s location on a plane.

## Basics of Coordinate Geometry

There are four quadrants along with their respective values in the graph of coordinate planes, as shown in Figure 1.2

- Quadrant 1 : (+x, +y)

In quadrant 1, the values of x and y are both positive.

- Quadrant 2 : (-x, +y)

In quadrant 2, the value of x is negative and y is positive.

- Quadrant 3 : (-x, -y) positive values of x and y

In quadrant 3, the values of x and y are both negative.

- Quadrant 4 : (+x, -y) positive values of x and y

In quadrant 4, the value of x is positive and y is negative.

Figure 1.2: Coordinate plane

Figure 1.2 shows the coordinate plane with a point (3,2), where ‘3’ is the x-coordinate and ‘2’ is the y-coordinate of the point on the coordinate plane.

### Distance Formula

We can easily calculate the distance between two points whose coordinates are given.

Let’s first calculate the distance of a point A (x1, y1) from the origin (0, 0)

Figure 1.3: Distance of a point from the origin

Let’s say the distance between point A and the origin is ‘d’. If we draw perpendiculars from point A to the x-axis and y-axis, we will get the distance from A to the x-axis as y_{1} and from A to the y-axis as x_{1}._{ }

Now, this makes a triangle, so using the **Pythagoras Theorem,** we can say:

The above theorem can be written as follows: one point is (x_{1}, y1), and the other is at the origin.

Thus, we can calculate the distance between any two points A (x1, y1) and B (x2, y2) in a coordinate plane using the graph in Figure 1.4

Figure 1.4: Distance between two points

Using Pythagoras theorem in the above graph, the distance between points A and B comes out to be:

The above formula is called the **distance formula**.

## Stay Tuned!!

Keep learning and keep implementing!!