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.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3264-1024x129.png)
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.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3264-1024x129.png)
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.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3416.png)
Example 2:
The picture below shows the grid map of a colony.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3265.png)
- Which building is located in Quadrant III?
- Which two places have the same x-coordinate?
Solution:
- The building located in Quadrant III:
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3265.png)
- 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).
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3266.png)
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.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3264-1024x129.png)
Example 4:
The following picture shows the grid map of a city.
- What are the coordinates of the location of the information center?
- What is located at (3/10 – 1/5) ?
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-87.jpeg)
Solution:
- Coordinates of the location of the information center:
- 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.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3272.png)
- Then use the y-coordinate of the point to move down following the y-axis as –0.2 is a negative value.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3267.png)
- Find the point on the coordinate plane. The coordinates (0.3, –0.2) are located at Start of Hiking Trail.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3268.png)
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?
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-88.jpeg)
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).
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3271-1024x562.png)
Exercise:
- What is the origin, and what are its coordinates?
- 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.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5373.png)
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.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5374.png)
4. Locate and label each point described by the ordered pairs below. Indicate which of the quadrants the points lie in.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5375.png)
- (𝟕, 𝟐)
- (𝟑, −𝟒)
5. Locate and label each point described by the ordered pairs below. Indicate which of the quadrants the points lie in.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5396.png)
- (𝟏, −𝟓)
- (−𝟑, 𝟖)
- (−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)
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5397.png)
8. Graph and label each point on the coordinate plane.
a. (−2.5, 1.5)
b. (3/4 , -1 ½ )
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5400.png)
9.The following picture shows the grid map of a city.
What are the coordinates of the location of Picnic Area 3?
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5402.png)
10. The following picture shows the grid map of a city. What is located at (-7/10, -1/5) ?
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5404.png)
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:
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3276-1024x337.png)
![Rational Numbers on The Coordinate Plane](/_next/image?url=https%3A%2F%2Fwww.turito.com%2Flearn-internal%2Fwp-content%2Fuploads%2F2022%2F09%2FRational-Numbers-on-The-Coordinate-Plane.png&w=1920&q=50)
Related topics
Addition and Multiplication Using Counters & Bar-Diagrams
Introduction: We can find the solution to the word problem by solving it. Here, in this topic, we can use 3 methods to find the solution. 1. Add using counters 2. Use factors to get the product 3. Write equations to find the unknown. Addition Equation: 8+8+8 =? Multiplication equation: 3×8=? Example 1: Andrew has […]
Read More >>Dilation: Definitions, Characteristics, and Similarities
Understanding Dilation A dilation is a transformation that produces an image that is of the same shape and different sizes. Dilation that creates a larger image is called enlargement. Describing Dilation Dilation of Scale Factor 2 The following figure undergoes a dilation with a scale factor of 2 giving an image A’ (2, 4), B’ […]
Read More >>How to Write and Interpret Numerical Expressions?
Write numerical expressions What is the Meaning of Numerical Expression? A numerical expression is a combination of numbers and integers using basic operations such as addition, subtraction, multiplication, or division. The word PEMDAS stands for: P → Parentheses E → Exponents M → Multiplication D → Division A → Addition S → Subtraction Some examples […]
Read More >>System of Linear Inequalities and Equations
Introduction: Systems of Linear Inequalities: A system of linear inequalities is a set of two or more linear inequalities in the same variables. The following example illustrates this, y < x + 2…………..Inequality 1 y ≥ 2x − 1…………Inequality 2 Solution of a System of Linear Inequalities: A solution of a system of linear inequalities […]
Read More >>Other topics
![demo](https://a.storyblok.com/f/128066/544x376/641160f2e6/learn_toast.webp)
Comments: