Choose the appropriate drawing where the dots appear: $$ (6,6),\lparen-3,0) $$

–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 –1 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 10 10 10 11 11 11 12 12 12 –6 –6 –6 –5 –5 –5 –4 –4 –4 –3 –3 –3 –2 –2 –2 –1 –1 –1 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6

Choose the appropriate drawing where the dots appear: $$ (1,3),\lparen2,5),(3,3) $$

–8 –8 –8 –7 –7 –7 –6 –6 –6 –5 –5 –5 –4 –4 –4 –3 –3 –3 –2 –2 –2 –1 –1 –1 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 10 10 10 11 11 11 –4 –4 –4 –3 –3 –3 –2 –2 –2 –1 –1 –1 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 0 0 0

–7 –7 –7 –6 –6 –6 –5 –5 –5 –4 –4 –4 –3 –3 –3 –2 –2 –2 –1 –1 –1 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 10 10 10 11 11 11 12 12 12 13 13 13 –5 –5 –5 –4 –4 –4 –3 –3 –3 –2 –2 –2 –1 –1 –1 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 0 0 0

Choose the appropriate drawing where the dots appear: $$ (-5,1),\lparen7,0),(-4,-1) $$

–7 –7 –7 –6 –6 –6 –5 –5 –5 –4 –4 –4 –3 –3 –3 –2 –2 –2 –1 –1 –1 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 10 10 10 11 11 11 12 12 12 13 13 13 –5 –5 –5 –4 –4 –4 –3 –3 –3 –2 –2 –2 –1 –1 –1 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 0 0 0

–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 –1 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 10 10 10 11 11 11 12 12 12 13 13 13 14 14 14 –6 –6 –6 –5 –5 –5 –4 –4 –4 –3 –3 –3 –2 –2 –2 –1 –1 –1 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7

Coordinate System Practice Problems & Exercises with Solutions

Understanding Coordinate System

Complete explanation with examples

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.

Detailed explanation

Practice Coordinate System

Test your knowledge with 2 quizzes

Choose the appropriate drawing where the dots appear:

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

Examples with solutions for Coordinate System

Step-by-step solutions included

Exercise #1

Which point is marked on the map?

Step-by-Step Solution

Answer:

$(5,3)$

Video Solution

Exercise #2

Which point is marked on the graph?

Step-by-Step Solution

Answer:

$(6,1)$

Video Solution

Exercise #3

Which figure shows the following points?

$(-4,4),(-2,2),(-4,-2)$

Step-by-Step Solution

Answer:

Video Solution

Exercise #4

Choose the figure that shows the following points:

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

Step-by-Step Solution

Answer:

Video Solution

Exercise #5

Choose the figure that shows the following points:

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

Step-by-Step Solution

Answer:

Video Solution

Frequently Asked Questions

Everything you need to know about Coordinate System

How do you find the coordinates of a point on a coordinate plane?

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To find coordinates, draw perpendicular lines from the point to both axes. The x-coordinate is where the vertical line meets the x-axis, and the y-coordinate is where the horizontal line meets the y-axis. Write the coordinates as (x, y) with the x-value first.

What are the four quadrants in a coordinate system?

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The four quadrants are: Quadrant I (positive x, positive y), Quadrant II (negative x, positive y), Quadrant III (negative x, negative y), and Quadrant IV (positive x, negative y). They are numbered counterclockwise starting from the upper right.

What coordinates do points on the axes have?

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Points on the x-axis have coordinates (x, 0) where the y-value is always 0. Points on the y-axis have coordinates (0, y) where the x-value is always 0. The origin has coordinates (0, 0).

How do you plot a point like (3, -2) on a coordinate grid?

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Start at the origin (0, 0). Move 3 units right along the x-axis since x = 3 is positive. Then move 2 units down since y = -2 is negative. Mark the point where you end up.

What is the origin in a coordinate system?

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The origin is the intersection point of the x-axis and y-axis, located at coordinates (0, 0). It serves as the reference point for all other coordinates on the plane and is typically labeled with the letter O.

Which quadrant contains the point (-4, 5)?

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The point (-4, 5) is in Quadrant II because it has a negative x-coordinate (-4) and a positive y-coordinate (5). Quadrant II contains all points with negative x-values and positive y-values.

How do coordinate systems help in real life?

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Coordinate systems are used in GPS navigation, computer graphics, architecture, engineering, and map reading. They provide a precise way to locate positions and describe relationships between objects in space.

What's the difference between x-coordinate and y-coordinate?

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The x-coordinate (first number) tells you how far to move horizontally from the origin - positive values go right, negative go left. The y-coordinate (second number) tells you how far to move vertically - positive values go up, negative go down.

Practice by Question Type

Choose your preferred learning style and practice format for fraction problems

Identifiying the correct point

Coordinate System Practice Problems & Exercises with Solutions

Understanding Coordinate System

Practice Coordinate System

Examples with solutions for Coordinate System

Frequently Asked Questions

How do you find the coordinates of a point on a coordinate plane?

What are the four quadrants in a coordinate system?

What coordinates do points on the axes have?

How do you plot a point like (3, -2) on a coordinate grid?

What is the origin in a coordinate system?

Which quadrant contains the point (-4, 5)?

How do coordinate systems help in real life?

What's the difference between x-coordinate and y-coordinate?

Practice by Question Type

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