🗺️ Coordinates
Read, plot and translate points on a first-quadrant grid!
📖 Learn
Coordinate concepts
✏️ Examples
Worked problems
🔬 Visualiser
Interactive grid
🎯 Practice
20 mixed questions
📖 Coordinates
1. The x-axis and y-axis
A coordinate grid has two axes:
- x-axis – the horizontal line (goes left and right)
- y-axis – the vertical line (goes up and down)
- They cross at the origin (0, 0)
First quadrant: both x and y are positive (≥ 0)
2. Reading Coordinates (x, y)
A point is written as (x, y).
"Along the corridor, then up the stairs"
- Go right along the x-axis first
- Then go up along the y-axis
Example: (3, 5) → go right 3, up 5.
3. Plotting Points
To plot the point (4, 2):
Start at the origin (0, 0)
Move 4 units to the right (x = 4)
Move 2 units up (y = 2)
Mark the point with a dot or cross
4. Missing Vertex of a Rectangle
If you have 3 corners of a rectangle, you can find the 4th:
Example: corners at (1,1), (4,1), (4,3). The missing corner shares x=1 with the first corner and y=3 with the third → missing vertex is (1, 3).
Rectangles have opposite sides that are equal and parallel
5. Translations
A translation moves a point without turning or flipping it.
- Move right → add to x
- Move left → subtract from x
- Move up → add to y
- Move down → subtract from y
New x = old x ± steps New y = old y ± steps
✏️ Worked Examples
Example 1 – Read the x-coordinate
Point A is at (3, 5). What is the x-coordinate?
The x-coordinate is the first number
x = 3
Example 2 – Read the y-coordinate
Point A is at (3, 5). What is the y-coordinate?
The y-coordinate is the second number
y = 5
Example 3 – Translate right
Point A is at (2, 3). Move 3 right. New x = ?
Move right → add to x: 2 + 3 = 5
New point: (5, 3)
Example 4 – Translate up
Point A is at (2, 3). Move 2 up. New y = ?
Move up → add to y: 3 + 2 = 5
New point: (2, 5)
Example 5 – Missing vertex
Rectangle corners: (1,1), (4,1), (4,3). Find missing corner.
Missing corner has same x as (1,1) → x = 1
Missing corner has same y as (4,3) → y = 3
Missing corner: (1, 3)
Exercise 1 – Read x-coordinates
Points: A(3,5) B(1,4) C(6,2) D(2,0) E(4,3) F(0,5) G(5,1) H(3,4) I(2,6) J(4,2). Enter the x-coordinate for each.
Exercise 2 – Read y-coordinates
Points: A(3,5) B(1,4) C(6,2) D(2,0) E(4,3) F(0,5) G(5,1) H(3,4) I(2,6) J(4,2). Enter the y-coordinate for each.