medium difficulty7 min

Cartesian Plane and Quadrants

The Cartesian plane is a flat plane formed by two perpendicular number lines, the x-axis and y-axis, meeting at the origin and dividing the plane into four quadrants.

In one line: Start top-right as I, then move anticlockwise: I, II, III, IV.

Practice This Concept

Understand it

The horizontal line is the x-axis and the vertical line is the y-axis.
Their meeting point is the origin (0, 0).
The four regions are called quadrants.
The signs of x and y decide the quadrant: I (+,+), II (-,+), III (-,-), and IV (+,-).

Example

The point (-3, 4) lies in Quadrant II because x is negative and y is positive.

Formula and rule

Quadrant I: (+,+), Quadrant II: (-,+), Quadrant III: (-,-), Quadrant IV: (+,-).

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

For (-5, -1), x is negative and y is negative.

1So the point is in Quadrant III.
2The actual distances from axes do not change the quadrant.

Method you can reuse

1Look at x first, then y.
2Match the sign pair with the quadrant list.
3If either coordinate is zero, the point is on an axis, not in a quadrant.

Sketch it in your answer

Draw perpendicular axes crossing at origin, mark arrows on positive x and positive y directions, and label the four quadrants anticlockwise from the top-right region.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

In which quadrant does the point (6, -2) lie, and why?

Think first, then show answer

The point (6, -2) lies in Quadrant IV because its x-coordinate is positive and its y-coordinate is negative.

Common wrong answer

Calling (-5, -1) Quadrant II because the first coordinate is negative is wrong; both signs must be checked.

Don't mix this up

Students sometimes decide the quadrant by the bigger number instead of using the signs of x and y.

Exam tip

For quadrant questions, check signs first and values later. The sign pattern is the fastest clue.