Coordinate System - Examples, Exercises and Solutions

Practice Coordinate SystemPractice Ordered pair
Question Types:
Ordered Pair: Identifiying the correct point

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:

coordinate system image

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

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

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

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

Detailed explanation

Practice Coordinate System

Question 1

Which point is marked on the graph?

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Question 2

Which point is marked on the map?

–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777–3–3–3–2–2–2–1–1–1111222333000

Question 3

Choose the appropriate drawing where the dots appear:

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

Question 4

Choose the appropriate drawing where the dots appear:

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

Question 5

Choose the appropriate drawing where the dots appear:

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

Examples with solutions for Coordinate System

Exercise #1

Which point is marked on the graph?

–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777–3–3–3–2–2–2–1–1–1111222333000

Video Solution

Answer

(6,1) (6,1)

Exercise #2

Which point is marked on the map?

–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777–3–3–3–2–2–2–1–1–1111222333000

Video Solution

Answer

(5,3) (5,3)

Exercise #3

Choose the appropriate drawing where the dots appear:

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

Video Solution

Answer

–8–8–8–7–7–7–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888999101010111111–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555000

Exercise #4

Choose the appropriate drawing where the dots appear:

(1,3),(2,5),(3,3) (1,3),\lparen2,5),(3,3)

Video Solution

Answer

–8–8–8–7–7–7–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888999101010111111–4–4–4–3–3–3–2–2–2–1–1–1111222333444555000

Exercise #5

Choose the appropriate drawing where the dots appear:

(−5,1),(7,0),(−4,−1) (-5,1),\lparen7,0),(-4,-1)

Video Solution

Answer

–7–7–7–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888999101010111111121212131313–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555000

Question 1

Choose the appropriate drawing where the dots appear:

\( (6,6),\lparen-3,0) \)

Question 2

Choose the figure that shows the following points:

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

Question 3

Choose the figure that shows the following points:

\( (2,-2),(-4,0),(0,3) \)

Question 4

Which figure shows the following points?

\( (-4,4),(-2,2),(-4,-2) \)

Exercise #6

Choose the appropriate drawing where the dots appear:

(6,6),(−3,0) (6,6),\lparen-3,0)

Video Solution

Answer

–10–10–10–9–9–9–8–8–8–7–7–7–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888999101010111111121212–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666

Exercise #7

Choose the figure that shows the following points:

(2,0),(2,4),(6,−2) (2,0),(2,4),(6,-2)

Video Solution

Answer

–3–3–3–2–2–2–1–1–1111222333444555666777888999–3–3–3–2–2–2–1–1–1111222333444000

Exercise #8

Choose the figure that shows the following points:

(2,−2),(−4,0),(0,3) (2,-2),(-4,0),(0,3)

Video Solution

Answer

–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777–2–2–2–1–1–1111222333444000

Exercise #9

Which figure shows the following points?

(−4,4),(−2,2),(−4,−2) (-4,4),(-2,2),(-4,-2)

Video Solution

Answer

–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777–2–2–2–1–1–1111222333444000