Geometry and measurement
Coordinate Plane Practice
Read and plot ordered pairs, find missing rectangle vertices, and explain horizontal and vertical distances with worked answers.
Grades 5–7 foundations · 6 questions · Free to print · Answers included
Make sense of the method
A coordinate pair tells you where a point is: move horizontally by x, then vertically by y. The origin is (0, 0).
These questions use the first quadrant and the axes. They build graph-reading foundations; negative coordinates and full transformation work need further practice.
- Find the origin and read the spacing of the grid.
- For (x, y), move x units to the right and y units up.
- Mark one point, label it, and check the coordinates in that order.
- For a horizontal or vertical distance, compare the coordinates that change.
A worked example
Plot K(3, 2). Describe how to reach K from the origin.
| Vertical y / horizontal x | x 0 | x 1 | x 2 | x 3 | x 4 | x 5 | x 6 | x 7 | x 8 | x 9 | x 10 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| y 10 | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty |
| y 9 | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty |
| y 8 | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty |
| y 7 | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty |
| y 6 | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty |
| y 5 | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty |
| y 4 | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty |
| y 3 | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty |
| y 2 | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty |
| y 1 | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty |
| y 0 | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty |
- The first coordinate, 3, is the horizontal movement.
- The second coordinate, 2, is the vertical movement.
- Mark their intersection and label it K.
K is 3 units right and 2 units up from (0, 0).
| Vertical y / horizontal x | x 0 | x 1 | x 2 | x 3 | x 4 | x 5 | x 6 | x 7 | x 8 | x 9 | x 10 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| y 10 | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty |
| y 9 | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty |
| y 8 | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty |
| y 7 | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty |
| y 6 | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty |
| y 5 | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty |
| y 4 | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty |
| y 3 | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty |
| y 2 | Empty | Empty | Empty | K | Empty | Empty | Empty | Empty | Empty | Empty | Empty |
| y 1 | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty |
| y 0 | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty | Empty |
Check the foundation before moving on
Cover the example and plot A(2, 5) on paper. Explain why the horizontal move is 2 and the vertical move is 5. Then plot B(5, 2): the points differ because the order matters. If you swap the coordinates, return to the origin and trace each move with a finger.
Once you can plot and explain both points, try the six questions below, including the missing rectangle vertex. Keep a short note of what you can explain and what needs another attempt. This first-quadrant practice does not establish readiness with negative coordinates or every kind of graph.
Next, use coordinates to describe translations and reflections. If negative values are unfamiliar, review integer number lines before working in all four quadrants.
For parents: ask the learner to explain the two moves. For independent study: write the explanation before checking the example. Your drawing and explanation are more informative than an answer alone.
Try the worksheet
Start with the first two questions, then build toward the final challenge. Show your method with calculations, drawings or a short explanation. These are practice questions with published answers, not a full-topic readiness check.
Build the foundation
1.Read the coordinates of P on the grid. Explain which coordinate you read first.
Read point P: accessible grid. Columns give horizontal x positions; rows give vertical y positions. Vertical y / horizontal x x 0 x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 y 10 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 9 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 8 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 7 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 6 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 5 Empty Empty P Empty Empty Empty Empty Empty Empty Empty Empty y 4 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 3 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 2 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 1 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 0 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Show your work on paper.Build the foundation
2.Plot A(6, 1) and B(1, 6). Explain why they are different points.
Plot A and B: accessible grid. Columns give horizontal x positions; rows give vertical y positions. Vertical y / horizontal x x 0 x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 y 10 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 9 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 8 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 7 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 6 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 5 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 4 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 3 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 2 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 1 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 0 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Show your work on paper.Strengthen your method
3.Plot R(0, 7) and S(4, 0). Name the axis containing each point.
Points on the axes: accessible grid. Columns give horizontal x positions; rows give vertical y positions. Vertical y / horizontal x x 0 x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 y 10 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 9 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 8 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 7 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 6 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 5 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 4 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 3 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 2 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 1 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 0 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Show your work on paper.Strengthen your method
4.C is at (2, 3) and D is at (8, 3). Draw the horizontal segment CD and find its length in grid units.
Horizontal segment endpoints: accessible grid. Columns give horizontal x positions; rows give vertical y positions. Vertical y / horizontal x x 0 x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 y 10 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 9 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 8 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 7 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 6 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 5 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 4 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 3 Empty Empty C Empty Empty Empty Empty Empty D Empty Empty y 2 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 1 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 0 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Show your work on paper.Apply and explain
5.A rectangle has consecutive vertices A(2, 2), B(7, 2), C(7, 6) and D. Find D and explain your reasoning.
Find the missing rectangle vertex: accessible grid. Columns give horizontal x positions; rows give vertical y positions. Vertical y / horizontal x x 0 x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 y 10 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 9 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 8 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 7 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 6 Empty Empty Empty Empty Empty Empty Empty C Empty Empty Empty y 5 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 4 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 3 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 2 Empty Empty A Empty Empty Empty Empty B Empty Empty Empty y 1 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 0 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Show your work on paper.Apply and explain
6.A robot starts at (1, 2), moves 5 units right, then 4 units up, then 2 units left. Plot its turning points and finish. What is the final point, and how many units did it travel?
Robot route planning grid: accessible grid. Columns give horizontal x positions; rows give vertical y positions. Vertical y / horizontal x x 0 x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 y 10 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 9 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 8 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 7 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 6 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 5 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 4 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 3 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 2 Empty O Empty Empty Empty Empty Empty Empty Empty Empty Empty y 1 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 0 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Show your work on paper.
Worked answers
Try the questions first. Then compare the reasoning, not just the final result.
Show all six worked solutions
1. P = (2, 5).
- P lines up with 2 on the horizontal axis.
- It lines up with 5 on the vertical axis.
- Write the horizontal coordinate first: (2, 5).
2. A is at (6, 1); B is at (1, 6).
- For A, move 6 right and 1 up.
- For B, move 1 right and 6 up.
- Reversing the coordinate order changes the horizontal and vertical positions.
Answer: A and B: accessible grid. Columns give horizontal x positions; rows give vertical y positions. Vertical y / horizontal x x 0 x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 y 10 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 9 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 8 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 7 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 6 Empty B Empty Empty Empty Empty Empty Empty Empty Empty Empty y 5 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 4 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 3 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 2 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 1 Empty Empty Empty Empty Empty Empty A Empty Empty Empty Empty y 0 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty 3. R lies on the y-axis; S lies on the x-axis.
- R has horizontal coordinate 0, so it stays on the vertical axis.
- S has vertical coordinate 0, so it stays on the horizontal axis.
- Zero is a coordinate, not an instruction to omit the point.
Answer: R and S: accessible grid. Columns give horizontal x positions; rows give vertical y positions. Vertical y / horizontal x x 0 x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 y 10 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 9 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 8 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 7 R Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 6 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 5 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 4 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 3 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 2 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 1 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 0 Empty Empty Empty Empty S Empty Empty Empty Empty Empty Empty 4. CD is 6 grid units long.
- Both points have y = 3, so the segment is horizontal.
- Subtract the x-coordinates: 8 − 2 = 6.
- Count the 6 unit intervals between C and D, not the number of grid lines touched.
5. D = (2, 6).
- D must have the same x-coordinate as A for the left side to be vertical.
- D must have the same y-coordinate as C for the top side to be horizontal.
- Combine those coordinates: D(2, 6). Join the four vertices in order to check.
Answer: all rectangle vertices: accessible grid. Columns give horizontal x positions; rows give vertical y positions. Vertical y / horizontal x x 0 x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 y 10 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 9 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 8 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 7 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 6 Empty Empty D Empty Empty Empty Empty C Empty Empty Empty y 5 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 4 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 3 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 2 Empty Empty A Empty Empty Empty Empty B Empty Empty Empty y 1 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 0 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty 6. The final point is (4, 6); the robot travelled 11 units.
- After moving right: (1 + 5, 2) = (6, 2).
- After moving up: (6, 2 + 4) = (6, 6).
- After moving left: (6 − 2, 6) = (4, 6).
- Total path length is 5 + 4 + 2 = 11 units. This is the route length, not the straight-line distance from start to finish.
Answer: robot route points: accessible grid. Columns give horizontal x positions; rows give vertical y positions. Vertical y / horizontal x x 0 x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 y 10 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 9 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 8 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 7 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 6 Empty Empty Empty Empty F Empty B Empty Empty Empty Empty y 5 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 4 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 3 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 2 Empty O Empty Empty Empty Empty A Empty Empty Empty Empty y 1 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty y 0 Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty Empty
Mistakes worth catching
Writing y before x.
Say “across, then up” and check the axis labels.
Counting grid lines instead of intervals.
A distance of one unit spans one space between neighbouring unit ticks.
Treating a route length as a direct distance.
Add the lengths of each move when the question asks how far the robot travelled.
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Skills covered
Geometry and measurement
- Read and plot ordered pairs in the first quadrant.
- Find missing rectangle vertices and horizontal or vertical distances.
Choose this practice by the skills you need. Grade placement and strand names vary between school systems; one worksheet covers selected skills rather than every expectation in a topic.
Related practice
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