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DETERMINING the COORDINATES, AXIS, QUADRANT, or LOCATION

Math Lesson

DETERMINING the COORDINATES, AXIS, QUADRANT, or LOCATION

Learn how to identify the coordinates, axis, quadrant, and exact location of any point on the Cartesian plane — clear, step-by-step, with worked examples!

Every point on the Cartesian plane has a home: an ordered pair (x, y), an axis, or a quadrant. Determine the signs of x and y, and you determine its location.
Look at (x, y) → Check the signs → Name the axis or quadrant!
O (0,0) I II III IV A(3,2) B(−3,2) C(−3,−2) D(3,−2) x y
The 4 quadrants and sample points — each color shows a different location!
QUADRANT I(+,  ) → x positive, y positive
QUADRANT II(−, +) → x negative, y positive
QUADRANT III(−, −) → x negative, y negative
QUADRANT IV(+, −) → x positive, y negative
Step 1: Read the Ordered Pair (x, y)

Every point is written as (x, y) — the first number is x (horizontal), the second number is y (vertical). The order matters!

Step 2: Check if the Point Lies on an Axis

If x = 0 → the point lies ON the y-axis (example: (0, 5)).
If y = 0 → the point lies ON the x-axis (example: (−4, 0)).
If both are 0 → the point is the ORIGIN (0, 0).

Points on the axes are NOT in any quadrant.

Step 3: Determine the Quadrant

If neither coordinate is zero, look at the signs of x and y:

(+, +) → Quadrant I    (right and up)
(−, +) → Quadrant II   (left and up)
(−, −) → Quadrant III   (left and down)
(+, −) → Quadrant IV    (right and down)

Step 4: Name the Location

Combine the results: say the coordinates, the axis (if on one), and the quadrant (if in one). Example: (−2, 5) is in Quadrant II, (0, −3) is on the y-axis.

Reverse: Find the Coordinates from a Location

If told "3 units right and 4 units up", the point is (3, 4).
If told "2 left, 5 down", the point is (−2, −5).
Right/Up = positive. Left/Down = negative.

5 Worked Examples
Example 1: Determine the location of (3, 5).

1. Neither coordinate is 0 → not on any axis.
2. x = 3 (positive) → right side.
3. y = 5 (positive) → upper side.
4. (+, +) → right and up.

Answer: Quadrant I
Example 2: Determine the location of (−4, 2).

1. Neither coordinate is 0 → not on any axis.
2. x = −4 (negative) → left side.
3. y = 2 (positive) → upper side.
4. (−, +) → left and up.

Answer: Quadrant II
Example 3: Determine the location of (−5, −3).

1. Neither coordinate is 0 → not on any axis.
2. x = −5 (negative) → left side.
3. y = −3 (negative) → lower side.
4. (−, −) → left and down.

Answer: Quadrant III
Example 4: Determine the location of (6, −4).

1. Neither coordinate is 0 → not on any axis.
2. x = 6 (positive) → right side.
3. y = −4 (negative) → lower side.
4. (+, −) → right and down.

Answer: Quadrant IV
Example 5: Determine the location of (0, −7).

1. x = 0 → the point lies ON an axis.
2. Since x = 0, the point is on the y-axis.
3. y = −7 → move 7 units down along the y-axis.
4. Not in any quadrant (points on axes never are).

Answer: On the y-axis
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 Determining Coordinates, Axis, Quadrant, and Location