Four-quadrant coordinates | Year 7

01 / LEARN

The idea, step by step

Two numbers identify one point

A coordinate pair is written $(x, y)$ . Start at the origin $(0, 0)$ . The first number tells you how far to move horizontally: positive is right and negative is left. The second tells you how far to move vertically: positive is up and negative is down.

The order matters. The points $(2, 4)$ and $(4, 2)$ have different locations. A coordinate records a position; it is not a calculation.

Quadrants and boundaries

Starting at the top-right and moving anticlockwise, the quadrant sign patterns are I $(+, +)$ , II $(-, +)$ , III $(-, -)$ and IV $(+, -)$ .

A point with $x = 0$ lies on the vertical axis. A point with $y = 0$ lies on the horizontal axis. Points on an axis do not lie inside a quadrant.

A common trap

Treating the first coordinate as the vertical move.

Instead: Read x first for left/right, then y for up/down.

02 / WORKED EXAMPLES

See the thinking

Example 1

Left, then up

Which quadrant contains $(- 3, 2)$ ?

The negative x-coordinate means 3 units left.
The positive y-coordinate means 2 units up.
Left and up is quadrant II.

Quadrant II.

Example 2

A point on a boundary

Describe the position of $(0, - 4)$ .

The x-coordinate is zero, so do not move left or right.
Move 4 units down.
The point lies on the negative part of the y-axis.

On the y-axis, not inside a quadrant.

Check your understanding

Which quadrant contains $(5, - 1)$ ?

Show answer

Quadrant IV.

Positive x is right and negative y is down.

03 / WORKSHEET

Your turn

6 questions · 12 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Describe the moves from the origin to $(4, 1)$ .
2 marks
Name the quadrant containing $(- 2, - 5)$ .
2 marks
A point is 3 left and 4 up from the origin. Write its coordinates.
2 marks
Which axis contains $(6, 0)$ ?
2 marks
Is the origin in quadrant I? Explain.
2 marks
Can a point with positive x and negative y lie in quadrant II? Explain.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Describe the moves from the origin to $(4, 1)$ .
2 marks
Read x=4 before y=1.
4 right, then 1 up.
Name the quadrant containing $(- 2, - 5)$ .
2 marks
Both coordinates are negative: left and down.
Quadrant III.
A point is 3 left and 4 up from the origin. Write its coordinates.
2 marks
Left gives x=-3; up gives y=4.
$(- 3, 4)$
Which axis contains $(6, 0)$ ?
2 marks
Its y-coordinate is zero.
The x-axis.
Is the origin in quadrant I? Explain.
2 marks
At (0,0), neither coordinate is positive or negative.
No. It lies on both axes.
Can a point with positive x and negative y lie in quadrant II? Explain.
2 marks
Quadrant II needs negative x and positive y.
No. Those signs place it in quadrant IV.

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Curriculum reference & lesson scope

Australian Curriculum v9.0 / South Australian Curriculum

Year 7 coordinate, pattern and authentic-graph interpretation scope. Includes prerequisite four-quadrant plotting; formal gradient/intercept techniques are not required here.

Official curriculum source ↗

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