Grid Coordinates
Learn to read, write and plot coordinates on a grid using ordered pairs.
What are Coordinates?
Coordinates are a pair of numbers that tell you the exact position of a point on a grid. We write them as (x, y) where x is the horizontal position (along) and y is the vertical position (up).
Always go ALONG first, then UP — (x, y)
Remember: “Along the corridor, then up the stairs!”
Reading a Coordinate Grid
Point A is at (2, 2) — 2 along, 2 up.
Point B is at (4, 4) — 4 along, 4 up.
Point C is at (3, 1) — 3 along, 1 up.
Plotting Points
To plot a point, start at the origin (0, 0) where the axes meet. Move right along the x-axis by the first number, then up by the second number. Mark the spot with a dot.
Example: Plot the point (3, 2)
Step 1: Start at (0, 0).
Step 2: Move 3 spaces right.
Step 3: Move 2 spaces up.
Mark the point!
Common mistake: Mixing up x and y! The point (3, 2) is different from (2, 3). Always remember: x comes first (along), then y (up).
Drawing Shapes with Coordinates
You can draw shapes by plotting several points and connecting them with straight lines. The coordinates tell you exactly where each corner goes.
Example: Draw a rectangle
Plot these points and join them in order: (1, 1), (4, 1), (4, 3), (1, 3)
Bottom-left: (1, 1)
Bottom-right: (4, 1)
Top-right: (4, 3)
Top-left: (1, 3)
This rectangle is 3 units wide and 2 units tall.
Area = 3 × 2 = 6 square units
Key Vocabulary
Coordinates
An ordered pair (x, y) that describes a point's position on a grid.
Origin
The point (0, 0) where the x-axis and y-axis meet.
x-axis
The horizontal line along the bottom of the grid (left to right).
y-axis
The vertical line along the side of the grid (up and down).
Worked Examples
What are the coordinates of a point that is 5 along and 3 up?
Step 1: The x-coordinate (along) is 5.
Step 2: The y-coordinate (up) is 3.
Answer: The coordinates are (5, 3).
Point P is at (2, 4) and Point Q is at (6, 4). What is the distance between them?
Step 1: Both points have the same y-coordinate (4), so they are on the same horizontal line.
Step 2: Distance = difference in x-coordinates: 6 − 2 = 4
Answer: The distance is 4 units.
Three corners of a square are (1, 1), (4, 1) and (4, 4). What is the fourth corner?
Step 1: A square has four corners. Three are given.
Step 2: The missing corner must complete the square: same x as (1,1) and same y as (4,4).
Answer: The fourth corner is (1, 4).
Knowledge Check
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Key Concepts Summary
- ●Coordinates are written as (x, y) — x is along, y is up.
- ●The origin is at (0, 0) where the two axes cross.
- ●Remember: “Along the corridor, up the stairs” to get the order right.
- ●(3, 2) and (2, 3) are different points — order matters!
- ●You can plot shapes by connecting coordinate points with straight lines.