Coordinate Plane: Free Interactive Coordinate Grid

What the coordinate plane is

The coordinate plane is two number lines crossing at a right angle. The horizontal one is the x-axis, the vertical one the y-axis, and they cross at the origin, (0, 0). Any point on the plane has an address: an ordered pair (x, y) that says how far to go across, then how far to go up or down. "Across first, then up" is the rule children repeat until it sticks; some teachers say "run before you jump" or "walk to the elevator, then ride it."

The axes cut the plane into four quadrants, numbered counterclockwise from the top right:

A point on an axis, like (0, 5) or (−2, 0), isn't in any quadrant. The readout says "on the y-axis" or "on the x-axis" for those.

How to plot points on a coordinate plane

1. Start at the origin. Every point is measured from (0, 0).
2. Read x first. Move right for a positive x, left for a negative x.
3. Then read y. Move up for a positive y, down for a negative y.
4. Mark the point. Label it with a letter so you can talk about it.

On this board, tap any grid point to plot it, or type the pair into Plot. The readout repeats the point and its quadrant, so a child who plotted (4, 3) when they meant (3, 4) sees the mistake right away. To move a point, drag it; it snaps to the nearest grid point.

Plotting points by grade

The Common Core standards build the coordinate plane over four years:

For 5th graders, switch to Quadrant I. For 6th grade and up, use all four.

Distance, midpoint and slope

When there are at least two points, the readout measures the last two:

• Distance. The board draws on the Pythagorean theorem and keeps the answer exact: from (−4, 2) to (6, 8), the legs are 10 and 6, so the distance is √136, which simplifies to 2√34, about 11.66.
• Midpoint. Average the x's and average the y's: ((−4 + 6) ÷ 2, (2 + 8) ÷ 2) = (1, 5).
• Slope. Rise over run: (8 − 2) ÷ (6 − (−4)) = 6/10 = 3/5. A vertical segment has no slope (it would mean dividing by zero), and the readout says so.

Points with the same x or the same y are a good place to start: from (2, 1) to (7, 1) the distance is just 7 − 2 = 5, the 6th-grade idea in 6.NS.C.8.

Drawing shapes and finding area

Turn on Connect points, plot the corners of a shape in order and press Close shape. The readout names the shape (rectangle, right isosceles triangle, parallelogram and so on) and gives its perimeter and area, both exact. Areas come from the shoelace formula, so they are always correct for lattice points, even for slanted shapes, and are whole numbers or halves. A rectangle from (1, 1) to (6, 4) has area 15 and perimeter 16.

Task card 11 asks for a triangle with area 6. There are many answers: a base of 4 and a height of 3, a base of 6 and a height of 2, or a slanted triangle whose area the board will check for you.

Reflections, rotations and translations

Pick a shape, choose a move and press Make image. The image appears in blue with primed labels, so A goes to A′. Compare the coordinates in the two shapes to find the rule:

Students can also plot the image themselves first and use Make image to check. The task cards accept either way: what matters is that the image is in the right place. Eighth graders learn that these moves keep lengths and angles the same (8.G.A.1), and the readout shows it: the image has the same perimeter and area as the original.

Activities to try

• Battleship. Each player secretly picks three points. Take turns calling out ordered pairs; plot each guess. The first to find all three wins.
• Quadrant sort. Plot one point in each quadrant, then one on each axis. Write the signs of each point and look for the pattern.
• Missing corner. Plot three corners of a rectangle. Where is the fourth? Task card 5 does this with a square.
• Same distance. Find all the grid points exactly 5 units from the origin. (There are twelve: four on the axes, and eight like (3, 4) and (−4, 3).)
• Shape makeover. Draw a triangle, then make its reflection, its rotation and a translation. Which images face the same way as the original?
• Mystery pictures. Plot a list of points in order to reveal a picture. Our coordinate grid pictures page has eight to try, with printable versions.

Tips for teachers and parents

• Say the order every time. "x first, then y" until students don't need it. Mixing up the order is the most common mistake.
• Start in quadrant I. Negative coordinates are easier once students are comfortable with positive ones.
• Connect to the number line. Each axis is just a number line. Students who know that −3 is left of 0 on a number line already know where x = −3 is.
• Predict before you press. Before making a reflection or rotation, ask students to predict where one point will go. NCTM's teaching practices emphasize this kind of reasoning: the board is for checking, not replacing it.
• Move to paper. Print a blank coordinate grid or a quadrant 1 grid for homework.

What makes this coordinate plane different

Most coordinate plane tools only plot points. This one also measures and transforms: exact distances as simplified square roots, midpoints, slopes, polygon names, perimeters and areas, plus reflections over both axes and y = x, three rotations and translations that label their images. It has quadrant I and four-quadrant grids with axes to 5, 10 or 20, tap-to-plot and typed points, drag-to-move with snapping, undo and redo, share links, a printable snapshot, keyboard controls and eleven self-checking task cards.

For geometry with pegs and rubber bands, try the geoboard. For algebra before graphing, try algebra tiles. Families comparing middle school programs can start with the best middle school math curriculum guide.

Choosing an activity

Grade bands describe possible curriculum connections, not an assessment of an individual learner. Start with an example the learner can explain, then change one feature at a time. The activity suggestions here are editorial teaching ideas, not results from a classroom trial of this software. Use the model alongside written work and physical materials when useful. The linked standards describe learning objectives; they do not endorse Edulist or require this particular tool.