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Rational Numbers on The Coordinate Plane with Example

Key Concepts

  • Graph points with integer coordinates
  • Locate and identify points with rational coordinates
  • Reflect points across the axes

Introduction: 

Coordinate plane: 

It is a grid containing two number lines that intersect at a right angle at 0. 

X-axis: 

The horizontal number line on the coordinate plane. 

Y-axis: 

The vertical number line on the coordinate plane. 

Quadrants: 

The four parts of the plane divided by x-axis and y-axis. The prefix “quad” means four. 

Origin: 

Center of the graph with coordinates (0, 0). 

The coordinate grid has an x-axis, a y-axis, an origin (0, 0), and four quadrants. Ordered pairs of rational numbers can be plotted just like ordered pairs of integers. 

Quadrant I: 

If a point is in quadrant I, the x-coordinate and the y-coordinate are positive. 

Quadrant II: 

If a point is in quadrant II, the x-coordinate is negative and the y-coordinate is positive. 

Quadrant III: 

Both the x-coordinate and y-coordinate of any point will be negative. 

Quadrant IV: 

If a point is in quadrant IV, the x-coordinate is positive and the y-coordinate is negative. 

Ordered pair: 

An ordered pair is a point in a coordinate plane. The ordered pair is represented in the form of (x, y). The first number corresponds to the x-coordinate and the second to the y-coordinate. 

2.4.1 Graph points with integer coordinates 

Example 1: 

Plot (4, –3) on the grid. 

Solution: 

To locate point (4, –3): 

Start at the origin, 

Move 4 units to the right on the x-axis. 

Then, move down 3 units on the y-axis. 

Example 2: 

The picture below shows the grid map of a colony. 

  1. Which building is located in Quadrant III? 
  1. Which two places have the same x-coordinate? 

Solution: 

  1. The building located in Quadrant III: 
  1. The two places that have the same x-coordinate:  

The coordinates of the club house are (12, 12). 

The coordinates of the swimming pool are (12, 8). 

2.4.2 Locate and identify points with rational coordinates 

Example 3: 

Plot (–2, –1½) on the grid. 

Solution: 

To locate point (–2, –1½): 

Start at the origin, 

Move 2 units to the left on the x-axis. 

Then, move down 1½ units on the y-axis. 

Example 4: 

The following picture shows the grid map of a city. 

  1. What are the coordinates of the location of the information center?  
  1. What is located at (3/10 – 1/5) ?

Solution: 

  1. Coordinates of the location of the information center: 
  1. Find the information center on the map. 
  • Follow the grid lines directly to the x-axis to find the x-coordinate, –0.2. 
  • Follow the grid lines directly to the y-axis to find the y-coordinate, 0.75. 

The coordinates of the location of the information center are (–0.2, 0.75). 

The same coordinates can also be represented using fractions as (–1/5, 3/4)

Located at (3/10, –1/5)

Convert the rational numbers into decimals, 

3/10 = 0.3 

–1/5 = –0.2  

Graph the point with coordinates (0.3, –0.2):  

  • Start at the origin, (0, 0).  
  • Use the x-coordinate of the point to move right along the x-axis as 0.3 is a positive value.  
  • Then use the y-coordinate of the point to move down following the y-axis as –0.2 is a negative value.  
  • Find the point on the coordinate plane. The coordinates (0.3, –0.2) are located at Start of Hiking Trail. 

2.4.3 Reflect points across the axes 

Example 5: 

Use the coordinate plane given below and find which picnic areas are located at points that are reflections of each other across one of the axes of the coordinate plane? 

Solution: 

The coordinates of the location of Picnic Area 1 are (-0.8, 6). 

The coordinates of the location of Picnic Area 4 are (-0.8, -6). 

Exercise:

  1. What is the origin, and what are its coordinates?
  2. Write ordered pairs that represent the location of points 𝑨 and 𝑩, where the first coordinate represents the horizontal direction, and the second coordinate represents the vertical direction.

3. Write ordered pairs that represent the location of points 𝑪, and 𝑫, where the first coordinate represents the horizontal direction, and the second coordinate represents the vertical direction.

4. Locate and label each point described by the ordered pairs below. Indicate which of the quadrants the points lie in.

  1. (𝟕, 𝟐)
  2. (𝟑, −𝟒)

5. Locate and label each point described by the ordered pairs below. Indicate which of the quadrants the points lie in.

  1. (𝟏, −𝟓)
  2. (−𝟑, 𝟖) 
  3. (−𝟐, −𝟏)

6. What do you know about the location of a point on the coordinate plane if both coordinates are positive?

7. Graph and label each point on the coordinate plane.
a.(−4, 1)
b.(4, 3)

8. Graph and label each point on the coordinate plane.
a. (−2.5, 1.5)
b. (3/4 , -1 ½ )

9.The following picture shows the grid map of a city.
What are the coordinates of the location of Picnic Area 3?

10. The following picture shows the grid map of a city. What is located at (-7/10, -1/5) ?

What have we learned:

  • Graph points with integer coordinates on a coordinate plane.
  • Locate and identify points with rational numbers on a coordinate plane.
  • Reflect points across the axes to find a mirror image across a line.

Concept Map: 

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