Coordinate Geometry

Coordinates give every point on a grid a precise location. Learn to read ordered pairs, plot points, recognise quadrants and use coordinates to describe shapes and movements.

Learning time: approximately 30 minutes · Curriculum-neutral

Learning Goals

Identify the x-axis, y-axis, origin and four quadrants.
Read and plot ordered pairs in the correct order.
Describe horizontal and vertical movement.
Use coordinates to identify shapes and reflected points.

1. The Cartesian Plane

The coordinate plane has two perpendicular number lines. The horizontal line is the x-axis; the vertical line is the y-axis. They meet at the origin, (0, 0).

A point is written as an ordered pair (x, y). The first number gives the horizontal position; the second gives the vertical position.

Example: (3, 2) means 3 units right and 2 units up from the origin.

2. The Four Quadrants

Quadrant	x sign	y sign	Example
I	Positive	Positive	(2, 3)
II	Negative	Positive	(−2, 3)
III	Negative	Negative	(−2, −3)
IV	Positive	Negative	(2, −3)

Quadrants are numbered anticlockwise starting at the top right. A point on an axis is not inside a quadrant.

3. Plot and Read Ordered Pairs

Start at (0, 0).
Move horizontally: right for positive x, left for negative x.
Move vertically: up for positive y, down for negative y.
Mark and label the point.

Example: To plot A(−4, 2), move 4 units left, then 2 units up.

Common mistake: (2, 5) and (5, 2) are different points. Always read x first, then y.

4. Horizontal and Vertical Distance

Points with the same y-coordinate lie on a horizontal line. Points with the same x-coordinate lie on a vertical line.

Horizontal example: A(−2, 3) and B(4, 3) are 4 − (−2) = 6 units apart.

Vertical example: C(5, −1) and D(5, 4) are 4 − (−1) = 5 units apart.

For points on the same horizontal or vertical line, distance is the absolute difference between the changing coordinates.

5. Describe Shapes with Coordinates

A rectangle with vertices (1, 1), (5, 1), (5, 3) and (1, 3) has width 4 units and height 2 units. Its perimeter is 2 × (4 + 2) = 12 units and its area is 4 × 2 = 8 square units.

Plot all vertices in order and join consecutive points to see the shape. Check that the final point joins back to the first.

6. Reflections in the Axes

Mirror line	Coordinate rule
x-axis	(x, y) → (x, −y)
y-axis	(x, y) → (−x, y)

Example: Reflect P(−3, 4) in the x-axis: P′ = (−3, −4). Reflect it in the y-axis: P″ = (3, 4).

Points on the mirror axis remain in the same position.

7. Check Your Understanding

Try the following before revealing the answers.

Which quadrant contains (−3, 5)?
Which quadrant contains (4, −2)?
Write the coordinates of the origin.
Find the horizontal distance between (−3, 2) and (5, 2).
Find the vertical distance between (4, −2) and (4, 6).

Show worked answers

Quadrant II.
Quadrant IV.
(0, 0).
5 − (−3) = 8 units.
6 − (−2) = 8 units.

9. Printable Worksheet

Learnora — Grade 7 Coordinate Geometry

Name: __________________________ Date: ______________

Name the quadrant of (6, −3).
Describe how to plot (−4, −2).
Find the vertical distance between (2, −5) and (2, 3).
Reflect (5, 6) in the y-axis.
A rectangle has corners (0, 0), (7, 0), (7, 2), (0, 2). Find its perimeter.

Teacher / Parent Answer Key

Quadrant IV.
Move 4 left and 2 down.
3 − (−5) = 8 units.
(−5, 6).
2 × (7 + 2) = 18 units.

Lesson Summary

Coordinates are written (x, y).
The origin is (0, 0).
Quadrants are identified by the signs of x and y.
Same y means horizontal; same x means vertical.
Reflections in axes change the sign of one coordinate.

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