MathematicsChapter 7: Coordinate Geometry
Four Quadrants
The two axes cut the plane into four quadrants, numbered anti-clockwise from the top-right.
Learning objectives
- Explain four quadrants in clear mathematical language
- Use the main rules and formulas in worked examples
- Recognise and correct common errors in this topic
What this grid covers
The two axes cut the plane into four quadrants, numbered anti-clockwise from the top-right. Quadrant I is ++ (x positive, y positive). Quadrant II is -+ (x negative, y positive). Quadrant III is -- (x negative, y negative). Quadrant IV is +- (x positive, y negative). Points on the axes are not inside a quadrant. Signs of (x,y) tell you the region before you plot.
Where / symbols
- Quadrant I
- Quadrant I is ++ (x positive, y positive).
- ++
- Quadrant I is ++ (x positive, y positive).
- II
- Quadrant II is -+ (x negative, y positive).
- -+
- Quadrant II is -+ (x negative, y positive).
What it means
The two axes cut the plane into four quadrants, numbered anti-clockwise from the top-right.
Main ideas
Quadrant I: ++ both positive; (3, 2) Quadrant II: -+ x negative, y positive; (-4, 1) Quadrant III: -- both negative; (-2, -5) Quadrant IV: +- x positive, y negative; (6, -3)
Why it matters
This method connects the definition to worked questions and later mathematics.
How to answer in an exam
I is ++; II is -+; III is --; IV is +-. Numbering is anti-clockwise from the positive x-axis region. Axis points have a zero and are not claimed by a quadrant. (x,y)=(y,x) still only when x=y, which in signs means the point lies on the line y=x through I and III.
Signs of x and y, starting from the top-right and turning anti-clockwise:
| Region | Signs (x, y) | A sample point |
|---|---|---|
| 1. Quadrant I | ++ both positive | (3, 2) |
| 2. Quadrant II | -+ x negative, y positive | (-4, 1) |
| 3. Quadrant III | -- both negative | (-2, -5) |
| 4. Quadrant IV | +- x positive, y negative | (6, -3) |
| 5. x-axis (not a quadrant) | y=0, x any | (4, 0) or (-1, 0) |
| 6. y-axis (not a quadrant) | x=0, y any | (0, 5) or (0, -2) |
In simple words
I is ++; II is -+; III is --; IV is +-. Numbering is anti-clockwise from the positive x-axis region. Axis points have a zero and are not claimed by a quadrant. (x,y)=(y,x) still only when x=y, which in signs means the point lies on the line y=x through I and III.
Key points
- Quadrant I
- ++
- II
- -+
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Four Quadrants
Sticky Notes · Quick Revision
Core Idea
- The two axes cut the plane into four quadrants, numbered anti-clockwise from the top-right.
Key Terms
- Quadrant I: Quadrant I is ++ (x positive, y positive).
- ++: Quadrant I is ++ (x positive, y positive).
Main Pattern
- Quadrant I: ++ both positive
- Quadrant II: -+ x negative, y positive
Worked Reminder
- Quadrant I: ++ both positive; (3, 2)
- Quadrant II: -+ x negative, y positive; (-4, 1)
- Quadrant III: -- both negative; (-2, -5)
Common Mistake
- I is ++; II is -+; III is --; IV is +-. Numbering is anti-clockwise from the positive x-axis region. Axis points have a zero and are not claimed by a quadrant. (x,y)=(y,x) still only when x=y, which in signs means the point lies on the line y=x through I and III.
Exam Tip
- State the rule for four quadrants, show each algebraic step, and check the final answer against the question.
60-second revision
- The two axes cut the plane into four quadrants, numbered anti-clockwise from the top-right.
- Quadrant I: ++ both positive; (3, 2)
- Quadrant II: -+ x negative, y positive; (-4, 1)
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