Coordinate Geometry • Topic 2 of 3

Quadrants and Their Signs

What are Quadrants?

The two axes divide the Cartesian plane into four regions called quadrants. They are numbered counterclockwise starting from the top-right quadrant.

Quadrant Signs:

Quadrantx-coordinatey-coordinateExample Point
**Quadrant II (QII)**Negative (-)Positive (+)(-4, 2)
**Quadrant III (QIII)**Negative (-)Negative (-)(-5, -3)
**Quadrant IV (QIV)**Positive (+)Negative (-)(6, -2)

Points on Axes:

  • Points on x-axis have y = 0 (example: (2, 0), (-5, 0))
  • Points on y-axis have x = 0 (example: (0, 3), (0, -4))
  • The origin (0, 0) belongs to both axes, not to any quadrant

Quick Memory Trick:

  • QI: (+, +) → "Both Positive"
  • QII: (-, +) → "Negative x, Positive y" → Think: "West, then North"
  • QIII: (-, -) → "Both Negative" → Think: "Southwest"
  • QIV: (+, -) → "Positive x, Negative y" → Think: "Southeast"
Distance FormulaA(x₁,y₁)B(x₂,y₂)dx₂ - x₁y₂ - y₁d = √[(x₂ - x₁)² + (y₂ - y₁)²]Derived from Pythagoras Theorem (hypotenuse of the right triangle)
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Worked Example

Solve a standard problem on Quadrants and Their Signs.

Solution

Apply the formula/method shown in the concept section above.

Key Points

  • Understand the definition and properties of Quadrants and Their Signs.
  • Study the worked examples and practice similar problems.
  • Always verify your answer using the original conditions.
Tap an option to check your answer0 / 4
Q1.In the first quadrant, the signs of $(x,y)$ are:
Explanation: Both positive.
Q2.The point $(-3,5)$ lies in quadrant:
Explanation: $(-,+)\Rightarrow$ II.
Q3.In quadrant III, the signs are:
Explanation: Both negative.
Q4.The point $(3,-7)$ lies in quadrant:
Explanation: $(+,-)\Rightarrow$ IV.