Graphs · The coordinate plane · 1.4

The four quadrants.

The axes split the plane into four quadrants, numbered I–IV counterclockwise from the top right. The signs of (x, y) tell you the quadrant: (+,+) is I, (−,+) II, (−,−) III, (+,−) IV.

01 / THE IDEA

See it work.

Watch the method

The four quadrants

(3, −2) is in Quadrant IV (+, −).

1 / 1
-6-666
1

Check the signs

x is +, y is −.

(3, −2)⇒IV(3,\, -2) \Rightarrow \text{IV}
— / WHY IT WORKS

The idea underneath.

Signs → quadrant

I (+,+) top-right, II (−,+) top-left, III (−,−) bottom-left, IV (+,−) bottom-right. On an axis → no quadrant.

Why it works

(+, −) is bottom-right = IV.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Which quadrant is (-4,6) in?

1

Answer

II

EX 2medium

Which quadrant is (-5,-2) in?

1

Answer

III

EX 3hard

Which quadrant is (3,5) in?

1

Answer

I

04 / COMMON TRAPS

Where students slip.

Trap

Numbering clockwise.

Fix

Quadrants go counterclockwise from top-right.

Trap

Putting an axis point in a quadrant.

Fix

A 0 coordinate sits on an axis, not in a quadrant.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Which quadrant is (5,2) in?

Need a hint?
  • Check the signs of x and y.
  • Match them to I–IV.
C2

Which quadrant is (3,6) in?

Need a hint?
  • Check the signs of x and y.
  • Match them to I–IV.
C3

Which quadrant is (1,3) in?

Need a hint?
  • Check the signs of x and y.
  • Match them to I–IV.
C4

Which quadrant is (6,2) in?

Need a hint?
  • Check the signs of x and y.
  • Match them to I–IV.
Apply

Apply (4)

A1

Which quadrant is (4,-5) in?

Need a hint?
  • Check the signs of x and y.
  • Match them to I–IV.
A2

Which quadrant is (4,-6) in?

Need a hint?
  • Check the signs of x and y.
  • Match them to I–IV.
A3

Which quadrant is (-5,1) in?

Need a hint?
  • Check the signs of x and y.
  • Match them to I–IV.
A4

Which quadrant is (1,-6) in?

Need a hint?
  • Check the signs of x and y.
  • Match them to I–IV.
Extension

Extension (4)

E1

Which quadrant is (3,3) in?

Need a hint?
  • Check the signs of x and y.
  • Match them to I–IV.
E2

Which quadrant is (-6,4) in?

Need a hint?
  • Check the signs of x and y.
  • Match them to I–IV.
E3

Which quadrant is (-6,6) in?

Need a hint?
  • Check the signs of x and y.
  • Match them to I–IV.
E4

Which quadrant is (-6,2) in?

Need a hint?
  • Check the signs of x and y.
  • Match them to I–IV.