🎯 Learning Outcomes

After completing this lesson, students will be able to:

✅ Define the Cartesian Plane.

✅ Identify the x-axis and y-axis.

✅ Locate the Origin.

✅ Understand positive and negative directions.

✅ Recognize how points are located in a plane.

🌟 Introduction

In the previous lesson, we learned that coordinates help us find the exact location of a place or object.

But where do we place these coordinates?

For this, we need a special system called the Cartesian Plane.

Think of a Cartesian Plane as a giant map made of two number lines crossing each other.

Using this plane, we can locate any point accurately.

📖 What is a Cartesian Plane?

A Cartesian Plane is a flat surface formed by two perpendicular number lines.

These lines intersect at a right angle (90°).

The Cartesian Plane is also known as:

• Coordinate Plane
• XY-Plane
• Coordinate System

It helps us locate points using coordinates.

📖 The Two Axes

The Cartesian Plane consists of two axes.

1. x-axis

The horizontal number line is called the x-axis.

It extends:

⬅ Left and Right ➡

2. y-axis

The vertical number line is called the y-axis.

It extends:

⬆ Up and Down ⬇

📖 The Origin

The point where the x-axis and y-axis meet is called the Origin.

The coordinates of the Origin are:

O (0,0)

The Origin is the starting point of the coordinate system.

📖 Positive and Negative Directions

Every axis has positive and negative directions.

On the x-axis

Example:

• 5 is right of origin
• -5 is left of origin

On the y-axis

Example:

• 4 is above origin
• -4 is below origin

📖 Structure of the Cartesian Plane

             +Y
              ↑
              |
              |
              |
 -X ----------O---------- +X
              |
              |
              |
              ↓
             -Y

Where:

O = Origin (0,0)

📖 Points on the x-axis

Any point on the x-axis has:

y = 0

General form:

(x,0)

Examples:

(4,0)

(-3,0)

(7,0)

📖 Points on the y-axis

Any point on the y-axis has:

x = 0

General form:

(0,y)

Examples:

(0,5)

(0,-2)

(0,8)

📖 Locating a Point

Suppose we have the point:

A(4,3)

Step 1:

Move 4 units along the x-axis.

Step 2:

Move 3 units upward along the y-axis.

You reach point A.

Thus A is located at:

(4,3)

🏠 Real-Life Connection

Imagine standing at the center of a city.

The center is the Origin.

If you move:

• 4 blocks east
• 3 blocks north

Your position becomes:

(4,3)

This is exactly how coordinates work.

💡 Fun Fact

The Cartesian Plane is named after the French mathematician

René Descartes

who developed the modern coordinate system.

📝 Key Terms

📌 Important Facts

✔ Cartesian Plane = Coordinate Plane

✔ Horizontal line = x-axis

✔ Vertical line = y-axis

✔ Origin = (0,0)

✔ Right and Up are positive.

✔ Left and Down are negative.

✔ Points on x-axis have y = 0.

✔ Points on y-axis have x = 0.

📚 Lesson Summary

The Cartesian Plane is formed by two perpendicular axes called the x-axis and y-axis.

Their point of intersection is called the Origin (0,0).

The Cartesian Plane allows us to locate points accurately using coordinates.

Positive values are measured to the right and upward, while negative values are measured to the left and downward.

✍️ Practice Questions

Fill in the Blanks

1. The horizontal axis is called the _________.

Answer: x-axis

2. The vertical axis is called the _________.

Answer: y-axis

3. The point where both axes meet is called the _________.

Answer: Origin

4. The coordinates of the Origin are _________.

Answer: (0,0)

5. Values to the right of the Origin are _________.

Answer: Positive

Short Answer Questions

1. What is a Cartesian Plane?
2. What is the x-axis?
3. What is the y-axis?
4. What is the Origin?
5. Why is the Cartesian Plane useful?

🎯 Quiz (10 Marks)

Question 1

The horizontal axis is called:

a) y-axis

b) z-axis

c) x-axis

d) origin

✅ Answer: c

Question 2

The vertical axis is called:

a) x-axis

b) y-axis

c) z-axis

d) graph

✅ Answer: b

Question 3

The coordinates of the Origin are:

a) (1,1)

b) (0,1)

c) (1,0)

d) (0,0)

✅ Answer: d

Question 4

Positive values on the x-axis are found:

a) Left of Origin

b) Above Origin

c) Right of Origin

d) Below Origin

✅ Answer: c

Question 5

Positive values on the y-axis are found:

a) Above Origin

b) Below Origin

c) Left

d) Right

✅ Answer: a

Question 6

Which point lies on the x-axis?

a) (0,5)

b) (4,0)

c) (3,2)

d) (1,1)

✅ Answer: b

Question 7

Which point lies on the y-axis?

a) (0,4)

b) (5,0)

c) (2,3)

d) (4,1)

✅ Answer: a

Question 8

The Cartesian Plane is also called:

a) Number Plane

b) Coordinate Plane

c) Algebra Plane

d) Decimal Plane

✅ Answer: b

Question 9

The Origin is the point where:

a) Two curves meet

b) Two circles meet

c) x-axis and y-axis intersect

d) Coordinates end

✅ Answer: c

Question 10

True or False:

Points on the x-axis have y-coordinate equal to zero.

✅ Answer: True

📄 Assignment Activity

Draw a Cartesian Plane in your notebook.

1. Mark the x-axis.
2. Mark the y-axis.
3. Mark the Origin.
4. Label positive and negative directions.
5. Plot the following points:
   • A(4,0)
   • B(0,5)
   • C(-3,0)
   • D(0,-4)

📸 Upload a photo or PDF of your work.