Coordinates
Cambridge IGCSE Mathematics (0580) · Unit 3: Coordinate geometry · 9 flashcards
Coordinates is topic 3.1 in the Cambridge IGCSE Mathematics (0580) syllabus , positioned in Unit 3 — Coordinate geometry , alongside Gradient and length and Equations of lines. In one line: A coordinate is a set of values that show an exact position on a coordinate plane. It's usually represented as an ordered pair (x, y), where x is the horizontal position and y is the vertical position.
This topic is examined across Paper 1 (Core) or Paper 2 (Extended) — non-calculator — and Paper 3 (Core) or Paper 4 (Extended) — calculator.
The deck below contains 9 flashcards — 5 definitions, 1 key concept and 3 application cards — covering the precise wording mark schemes reward. Use the 5 definition cards to lock down command-word answers (define, state), then move on to the concept and application cards to handle explain, describe and compare questions.
The term 'coordinate' in the context of a Cartesian plane
A coordinate is a set of values that show an exact position on a coordinate plane. It's usually represented as an ordered pair (x, y), where x is the horizontal position and y is the vertical position.
Questions this Coordinates deck will help you answer
- › What is an 'ordered pair', and why is the order important?
- › Explain how to plot the point A(4, -2) on a coordinate plane.
- › A point B has coordinates (-3, 5). In which quadrant is point B located?
- › Describe how to determine the coordinates of a point that has already been plotted on a graph.
Define the term 'coordinate' in the context of a Cartesian plane.
A coordinate is a set of values that show an exact position on a coordinate plane. It's usually represented as an ordered pair (x, y), where x is the horizontal position and y is the vertical position.
What is an 'ordered pair', and why is the order important?
An ordered pair (x, y) represents a point on a coordinate plane. The order matters because (2, 3) is a different point than (3, 2). The first value is always the x-coordinate and the second value is the y-coordinate.
Describe the difference between the x-coordinate and the y-coordinate.
The x-coordinate represents the horizontal distance of a point from the origin along the x-axis. The y-coordinate represents the vertical distance of a point from the origin along the y-axis.
Explain how to plot the point A(4, -2) on a coordinate plane.
To plot A(4, -2), start at the origin (0, 0). Move 4 units to the right along the x-axis, then 2 units down parallel to the y-axis. Mark the point at this location.
Name the four quadrants of a Cartesian plane and describe the signs of the x and y coordinates in each.
Quadrant I: (+, +), Quadrant II: (-, +), Quadrant III: (-, -), Quadrant IV: (+, -). The signs indicate whether the x and y coordinates are positive or negative in each quadrant.
What are the coordinates of the 'origin'?
The origin is the point where the x-axis and y-axis intersect. Its coordinates are (0, 0). It serves as the reference point for plotting other coordinates.
Describe what is meant by the 'axes' of a coordinate plane.
The axes of a coordinate plane are the horizontal x-axis and the vertical y-axis. These axes are perpendicular to each other and divide the plane into four quadrants.
A point B has coordinates (-3, 5). In which quadrant is point B located?
Point B (-3, 5) is located in Quadrant II. This is because the x-coordinate is negative and the y-coordinate is positive in Quadrant II.
Describe how to determine the coordinates of a point that has already been plotted on a graph.
To find the coordinates of a plotted point, draw a vertical line to the x-axis to find the x-coordinate and a horizontal line to the y-axis to find the y-coordinate. The coordinates are then written as (x, y).
Key Questions: Coordinates
Define the term 'coordinate' in the context of a Cartesian plane.
A coordinate is a set of values that show an exact position on a coordinate plane. It's usually represented as an ordered pair (x, y), where x is the horizontal position and y is the vertical position.
Describe the difference between the x-coordinate and the y-coordinate.
The x-coordinate represents the horizontal distance of a point from the origin along the x-axis. The y-coordinate represents the vertical distance of a point from the origin along the y-axis.
Name the four quadrants of a Cartesian plane and describe the signs of the x and y coordinates in each.
Quadrant I: (+, +), Quadrant II: (-, +), Quadrant III: (-, -), Quadrant IV: (+, -). The signs indicate whether the x and y coordinates are positive or negative in each quadrant.
What are the coordinates of the 'origin'?
The origin is the point where the x-axis and y-axis intersect. Its coordinates are (0, 0). It serves as the reference point for plotting other coordinates.
Describe what is meant by the 'axes' of a coordinate plane.
The axes of a coordinate plane are the horizontal x-axis and the vertical y-axis. These axes are perpendicular to each other and divide the plane into four quadrants.
More topics in Unit 3 — Coordinate geometry
Coordinates sits alongside these Mathematics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.
Cambridge syllabus keywords to use in your answers
These are the official Cambridge 0580 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.
Key terms covered in this Coordinates deck
Every term below is defined in the flashcards above. Use the list as a quick recall test before your exam — if you can't define one of these in your own words, flip back to that card.
Related Mathematics guides
Long-read articles that go beyond the deck — cover the whole subject's common mistakes, high-yield content and revision pacing.
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