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Coordinates
Year 7 • Coordinates
Lesson: Coordinates – Reading and Plotting Points
Learn how to read, write, and plot coordinates on a grid. In this lesson, we explore the x-axis and y-axis, the coordinate plane,
and how to describe the position of points clearly and accurately – perfect for Year 7 students.
Lesson Objectives
- Understand what coordinates are and how they are written.
- Identify and label the x-axis and y-axis on a coordinate grid.
- Plot points in the first quadrant using ordered pairs (x, y).
- Read coordinates of points that are already drawn on a grid.
- Recognise and use all four quadrants of the coordinate plane (extension).
1. What Is a Coordinate Grid?
A coordinate grid (or coordinate plane) is made up of two number lines:
- The x-axis – the horizontal line (left and right).
- The y-axis – the vertical line (up and down).
Where the two axes cross is called the origin.
The origin has coordinates (0, 0).
The origin has coordinates (0, 0).
2. Reading and Writing Coordinates (x, y)
A coordinate is written as an ordered pair in brackets: (x, y).
- The first number is the x-coordinate – how far you move left or right.
- The second number is the y-coordinate – how far you move up or down.
Important: The order always matters:
(x, y) = (along, then up)
First move along the x-axis, then move up or down along the y-axis.
(x, y) = (along, then up)
First move along the x-axis, then move up or down along the y-axis.
3. Plotting Points in the First Quadrant
In the first quadrant, both x and y are positive. This is usually the top-right section of the grid.
Example:
Plot the point (4, 2).
Plot the point (4, 2).
Step 1: Start at the origin (0, 0).
Step 2: Move 4 units to the right (along the x-axis).
Step 3: From there, move 2 units up (along the y-axis).
Mark the point and label it A(4, 2).
Example:
Plot the points B(1, 5), C(3, 3), and D(6, 1).
Each time, remember: across first, then up.
Plot the points B(1, 5), C(3, 3), and D(6, 1).
Each time, remember: across first, then up.
4. Using All Four Quadrants (Extension)
If the grid includes negative numbers, the coordinate plane is split into four quadrants:
- Quadrant I (top-right): x positive, y positive e.g. (3, 4)
- Quadrant II (top-left): x negative, y positive e.g. (−2, 5)
- Quadrant III (bottom-left): x negative, y negative e.g. (−3, −1)
- Quadrant IV (bottom-right): x positive, y negative e.g. (4, −2)
Example:
A point at (−4, 2) is in Quadrant II because x is negative and y is positive.
A point at (3, −5) is in Quadrant IV because x is positive and y is negative.
A point at (−4, 2) is in Quadrant II because x is negative and y is positive.
A point at (3, −5) is in Quadrant IV because x is positive and y is negative.
5. Real-Life Example with Coordinates
On a simple map of a theme park, each attraction can be marked by coordinates.
• Roller coaster: (2, 6)
• Food stall: (5, 3)
• Entrance: (0, 0)
(a) Which attraction is highest up on the map?
(b) Which attraction is farthest to the right?
(c) What are the coordinates of an attraction that is 4 units to the right and 2 units up from the entrance?
(Answers are in the Answer Key section below.)
Practice Questions
A. Reading Coordinates
Imagine the following points are already drawn on a coordinate grid. Write their coordinates.
- Point A is 3 units to the right and 4 units up from the origin.
- Point B is 6 units to the right and 1 unit up from the origin.
- Point C is 2 units to the right and 7 units up from the origin.
- Point D is at the origin.
B. Plotting Points (First Quadrant)
On squared paper or a coordinate grid, plot these points and label them clearly.
- A(2, 5)
- B(6, 3)
- C(1, 7)
- D(4, 1)
- E(5, 5)
Then join A → B → C → D → E in order. What shape or pattern does it look like?
C. Coordinates in All Four Quadrants (Extension)
State which quadrant each point is in.
- P(3, 4)
- Q(−2, 5)
- R(−4, −1)
- S(5, −3)
- T(0, −4) – Is this in a quadrant or on an axis?
D. Describe the Movement
Each time, describe how you move from the first point to the second point.
- From (2, 3) to (5, 3)
- From (4, 1) to (4, 6)
- From (1, 5) to (4, 2)
- From (−2, −1) to (1, −1)
E. Word Problems with Coordinates
-
A robot starts at (0, 0). It moves 4 units to the right and 3 units up.
(a) What are its new coordinates?
Then it moves 2 units left and 1 unit down.
(b) What are its final coordinates? -
A treasure map uses coordinates. The clue says:
“Go to a point 5 units to the right and 2 units down from the origin.”
(a) Write the coordinates of the treasure.
(b) Is this point in the first, second, third, or fourth quadrant?
✅ Show Answer Key
A. Reading Coordinates
- A is 3 right and 4 up → (3, 4)
- B is 6 right and 1 up → (6, 1)
- C is 2 right and 7 up → (2, 7)
- D is at the origin → (0, 0)
B. Plotting Points (First Quadrant)
Points should all be in the first quadrant:
A(2, 5), B(6, 3), C(1, 7), D(4, 1), E(5, 5).
The joined shape will look like a simple polygon (students’ descriptions may vary – accept sensible answers).
C. Coordinates in All Four Quadrants
- P(3, 4): x positive, y positive → Quadrant I
- Q(−2, 5): x negative, y positive → Quadrant II
- R(−4, −1): x negative, y negative → Quadrant III
- S(5, −3): x positive, y negative → Quadrant IV
- T(0, −4): on the y-axis, not in any quadrant.
D. Describe the Movement
- (2, 3) → (5, 3): move 3 units right.
- (4, 1) → (4, 6): move 5 units up.
- (1, 5) → (4, 2): move 3 units right and 3 units down.
- (−2, −1) → (1, −1): move 3 units right.
E. Word Problems with Coordinates
-
Robot:
Start at (0, 0).
Move 4 right, 3 up → (4, 3).
Then 2 left, 1 down → x: 4 − 2 = 2, y: 3 − 1 = 2 → final point (2, 2). -
Treasure:
5 right and 2 down from origin → x = 5, y = −2 → (5, −2).
x positive, y negative → Quadrant IV.
Real-Life Example (Theme Park)
-
Highest up: compare y-values:
Roller coaster (2, 6), Food stall (5, 3), Entrance (0, 0).
Highest y is 6 → Roller coaster. -
Farthest right: compare x-values:
2, 5, 0 → biggest is 5 → Food stall. - 4 units right and 2 units up → (4, 2).
© Aviate Learning – Coordinates (Year 7)