Knowledge Organiser: Coordinates
Part of Coordinates · GCSE GCSE Mathematics revision
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.
Topic position
Section 8 of 8
Practice
10 questions
Recall
20 flashcards
Knowledge Organiser: Coordinates
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
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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
10 questions on Coordinates — practise free
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