Math Lesson

PARTS of the CARTESIAN PLANE

Get to know the x-axis, y-axis, origin, quadrants, and ordered pairs — the building blocks of the coordinate plane!

The Cartesian Plane is formed by two perpendicular number lines that intersect at a point called the origin, dividing the plane into four regions called quadrants.

x-axis ⊥ y-axis → Origin (0, 0) → 4 Quadrants

The Cartesian Plane with its parts labeled

X-Axis (Horizontal Axis)

The x-axis is the horizontal number line of the Cartesian plane. It runs from left to right. Numbers to the right of the origin are positive, while numbers to the left are negative.

Y-Axis (Vertical Axis)

The y-axis is the vertical number line of the Cartesian plane. It runs up and down. Numbers above the origin are positive, while numbers below are negative.

Origin

The origin is the point where the x-axis and y-axis intersect (meet). Its coordinates are (0, 0). It is the starting point or reference point of the Cartesian plane.

Quadrants

The two axes divide the plane into four regions called quadrants. They are numbered using Roman numerals:

Quadrant I → upper right (x+, y+)
Quadrant II → upper left (x−, y+)
Quadrant III → lower left (x−, y−)
Quadrant IV → lower right (x+, y−)

Ordered Pair (x, y)

A point on the Cartesian plane is described by an ordered pair (x, y).

The first number is the x-coordinate (abscissa) — how far left or right.
The second number is the y-coordinate (ordinate) — how far up or down.

Example: In (3, 4), the x-coordinate is 3 and the y-coordinate is 4.

4 Worked Examples

Example 1: Which axis is horizontal?

The horizontal line that runs left to right is the x-axis.

Answer: X-axis

Example 2: What are the coordinates of the origin?

The origin is where the x-axis and y-axis meet. Both values are zero.

Answer: (0, 0)

Example 3: In which quadrant does the point (3, 4) lie?

x = 3 (positive, right side)
y = 4 (positive, upper side)
Right and up → upper right region

Answer: Quadrant I

Example 4: In the ordered pair (5, −2), which is the y-coordinate?

The ordered pair is written as (x, y).
The second number is the y-coordinate.

Answer: −2

Guided Practice

Try It Yourself!

Answer all 3 guided questions. Hints and solutions are available if you need them!

NOTE: Correct answers will turn GREEN so you know your answer is correct!

Mastery Check

Quick Quiz Time!

Answer all 10 questions in one go. Good luck!

Please answer ALL questions before submitting!

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Made for students who want to master the Parts of the Cartesian Plane