Key Terms
- Coordinates: A pair (x, y) that gives the position of a point on a grid
- x-coordinate: Horizontal distance from the origin (positive = right)
- y-coordinate: Vertical distance from the origin (positive = up)
- Origin: The point (0, 0) where the x-axis and y-axis cross
- Quadrant: One of the four regions of the coordinate grid
- Midpoint: The exact middle point of a line segment
Must-Know Facts
- Always write coordinates as (x, y) — x first (across), then y (up)
- Quadrant 1: (+, +); Quadrant 2: (−, +); Quadrant 3: (−, −); Quadrant 4: (+, −)
- Negative x-coordinate means left of the y-axis; negative y means below the x-axis
- The origin (0, 0) belongs to neither axis quadrant
- Points on the x-axis always have y = 0; points on the y-axis always have x = 0
- Memory aid: "Along the corridor, then up the stairs" — x before y
Key Formulas
- Midpoint of (x₁, y₁) and (x₂, y₂) = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2)
- Distance between two points = √[(x₂ − x₁)² + (y₂ − y₁)²]
- To find distance without the formula: use Pythagoras on the horizontal and vertical gaps
Common Mistakes
- x before y: Coordinates are always (x, y) — across first, then up/down
- Negative coordinates: (−3, 2) means 3 left and 2 up — both the sign and direction must be correct
- Midpoint formula: Average the x-values AND the y-values separately — don't add all four numbers and divide by 4
- Distance formula sign: (x₂ − x₁)² is always positive (squared) — negative differences work fine under the square root
This topic summary covers Knowledge Organiser: Coordinates within Coordinates for GCSE Mathematics. Revise Coordinates in Graphs for GCSE Mathematics with 10 exam-style questions and 20 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 8 of 8 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Practice questions for Coordinates
Which point has coordinates (–3, 5)?
A triangle has vertices at P(−1, 2), Q(3, 5) and R(7, 2). Show that the triangle is isosceles.
Quick recall flashcards
Which axis is vertical?
The y-axis is the vertical axis (runs up and down).
What are coordinates?
A pair of numbers (x, y) that describe the exact position of a point on a coordinate plane.