# Coordinate System - Examples, Exercises and Solutions

What is the coordinate system?

A coordinate system, or more precisely, a Cartesian coordinate system, is a method to precisely present the position of points, whether on a plane (two-dimensional) or in three-dimensional space. In this chapter, we will focus on a coordinate system on a plane, that is, a system made up of two axes (straight lines) that are perpendicular to each other (forming a 90-degree angle between them).

To facilitate the understanding of the material, let's look at the following drawing, which gives an example of a two-dimensional coordinate system:

As mentioned, as can be seen in the drawing, it is customary to identify the horizontal axis with $X$ and the vertical axis with $Y$.

The intersection point between the two axes is called the origin and is usually identified with the letter $O$.

Along the $X$ horizontal axis, the numbers increase to the right of the origin and decrease to the left of the origin.

Along the $Y$ vertical axis, the numbers increase upwards in relation to the origin and decrease downwards in relation to the origin.

## examples with solutions for coordinate system

### Exercise #1

Which point is marked on the map?

### Video Solution

$(5,3)$

### Exercise #2

Which point is marked on the graph?

### Video Solution

$(6,1)$

### Exercise #3

Choose the appropriate drawing where the dots appear:

$(1,3),\lparen2,5),(3,3)$

### Exercise #4

Choose the appropriate drawing where the dots appear:

$(1,0),\lparen-2,-2),(-5,4)$

### Exercise #5

Choose the figure that shows the following points:

$(2,0),(2,4),(6,-2)$

### Video Solution

$(-5,1),\lparen7,0),(-4,-1)$