Coordinate grid: how to plot and read points, ordered pairs (x before y, "along the corridor, up the stairs"), the four quadrants and their signs, the axes and the origin, distance between points, reflections across the axes, the midpoint, the mistakes, and printable coordinate grid paper in three sizes

"Coordinate grid" is searched about 11,000 times a month in the United States, mostly by Grade 5 and 6 students and their parents looking for two things: the rules for plotting a point and a sheet of grid paper to print. This page gives both. The rules in full (the axes, the ordered pair, the three plotting steps, the four quadrants and their signs, points on the axes), then distance, reflection and midpoint for Grade 6 to 8, the mistakes, the curriculum placements, and a printable with coordinate grid paper in three sizes and a practice set.

Download the coordinate grid paper and practice (PDF) (A4, a first-quadrant 0 to 10 grid and a four-quadrant −10 to 10 grid with the rules on page 1, a 1 cm squared grid with the practice set and answers on page 2, free).

The parts of the grid

How to plot a point in three steps

To plot (4, 3):

1. Put your pencil on the origin (0, 0).
2. Move along the x-axis 4 units to the right (the first number).
3. Move up 3 units (the second number), parallel to the y-axis. Mark the point and label it (4, 3).

To plot (−2, −5): left 2, down 5. To plot (0, 6): no move across, up 6: the point sits on the y-axis. To plot (−7, 0): left 7, no move up: on the x-axis.

The order never changes: x first, then y. "Along the corridor, then up the stairs" (British classrooms) or "run before you jump" (American) are the memory lines; "x is a cross, so x goes across" settles which letter is which.

How to read a point

Reverse the steps. From the point, go straight down (or up) to the x-axis and read the number: that is x. Go straight across to the y-axis and read the number: that is y. Write them in brackets with a comma, x first. A point 3 to the left of the y-axis and 2 above the x-axis is (−3, 2).

The four quadrants and their signs

The numbering runs anticlockwise starting from the top right, the way angles are measured. Points on an axis belong to no quadrant: (0, 4) is on the y-axis, (−6, 0) on the x-axis, (0, 0) is the origin.

Grade 5 works in the first quadrant only (all coordinates positive); Grade 6 opens up all four with negative numbers.

Distance between points

• Same horizontal line (same y): subtract the x-coordinates. From (−3, 4) to (5, 4): 5 − (−3) = 8 units. Or count the grid squares.
• Same vertical line (same x): subtract the y-coordinates. From (2, −1) to (2, 6): 6 − (−1) = 7 units.
• Neither (Grade 8, GCSE): draw the right-angled triangle and use Pythagoras. From (1, 2) to (4, 6): across 3, up 4, distance √(3² + 4²) = 5 units. The general formula is d = √((x₂ − x₁)² + (y₂ − y₁)²).

A rectangle with corners (−2, 1), (4, 1), (4, 5), (−2, 5) has width 6 and height 4: area 24 square units, perimeter 20. Coordinate geometry questions in Grade 6 are almost all of this shape.

Reflections across the axes

• Reflect in the x-axis: the y-coordinate changes sign. (3, 5) → (3, −5).
• Reflect in the y-axis: the x-coordinate changes sign. (3, 5) → (−3, 5).
• Reflect in both (a half-turn about the origin): both change sign. (3, 5) → (−3, −5).

So the four points (±3, ±5) are the same point reflected into each quadrant, which is the Grade 6 standard 6.NS.6b in one sentence.

The midpoint

The midpoint of two points is the average of their coordinates: M = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2). Between (−2, 3) and (6, 7): ((−2 + 6) ÷ 2, (3 + 7) ÷ 2) = (2, 5). Used from Grade 8 and in GCSE for the centre of a line segment and the centre of a circle from a diameter.

The mistakes that cost marks

• Swapping x and y: (2, 5) plotted at (5, 2).
• Starting from the corner of the paper instead of the origin.
• Counting lines instead of gaps (the first grid line after 0 is 1, not 2).
• Missing a negative sign in quadrants II, III and IV.
• Writing the pair without brackets or without the comma.
• Numbering quadrants clockwise. It is anticlockwise from the top right.
• Choosing an uneven scale on a hand-drawn grid: every gap on an axis must be the same size.

Where it sits in each curriculum

Practice (answers in the PDF)

1. Plot and label A(2, 4), B(−3, 4), C(−3, −1), D(2, −1). What shape is ABCD, and what is its area?
2. In which quadrant is each point: (−4, 7), (5, −2), (−1, −9), (6, 3)? Which quadrant is (0, −5) in?
3. What is the distance from (−6, 2) to (3, 2)?
4. Reflect (−4, 7) in the x-axis, then in the y-axis. Give both results.
5. Find the midpoint of (−5, 2) and (3, −6).
6. A point is 4 units left of the y-axis and on the x-axis. Write its coordinates.

Download the grid paper and the practice set (PDF)

Where to get help

A 1-on-1 online maths class with a tutor who holds a master's in mathematics and teaches US Grades 5 to 8, KS2 and KS3, the Australian Years 5 to 7 and CBSE Class 9 and 10 every week: the coordinate plane taught with a shared grid on screen, every point plotted by the child and read back, so the x-before-y habit sets before straight-line graphs begin. The Grade 6 maths page lists the units; the free 30-minute first class is a real lesson on this week's homework. The next pages in this set are graphing linear equations and graphing proportional relationships.

Questions parents ask

See how we teach this, 1-on-1 online →