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§ Geometry

Coordinates (First Quadrant)

§ Geometry

Coordinates (First Quadrant)

CCSS.5.GCCSS.6.NS3 min read

Coordinates in the first quadrant represent the position of points on a grid using two positive numbers written as (x, y). The x-coordinate indicates the horizontal distance from the origin, whilst the y-coordinate shows the vertical distance upward. In Year 4 of the UK National Curriculum, pupils learn to describe positions on 2D grids using these coordinate pairs.

§ 01

Why it matters

Coordinate systems appear throughout daily life and advanced mathematics. Maps use grid references to locate places — the Ordnance Survey uses a coordinate system where London's centre sits at approximately (530000, 180000). Computer screens display images using pixel coordinates, with a typical smartphone screen containing over 2 million coordinate positions. Video games track character movement through 3D coordinate systems. In GCSE Mathematics, coordinates extend into negative values and coordinate geometry, including finding midpoints, gradients, and equations of lines. Engineering applications rely on precise coordinate measurements — aircraft navigation systems use coordinates to plot flight paths across thousands of kilometres. Even simple tasks like arranging desks in a classroom or planning a garden layout involve informal coordinate thinking.

§ 02

How to solve coordinates (first quadrant)

Coordinates — First Quadrant

  • A point is written as (x, y).
  • x = horizontal distance from origin (along).
  • y = vertical distance from origin (up).
  • The origin is (0, 0).

Example: Point (3, 5): go 3 right, 5 up.

§ 03

Worked examples

Beginner§ 01

What are the coordinates of point A?

Answer: (7, 5)

  1. Read the x-coordinate (horizontal position) → x = 7 — Point A is 7 units to the right of the origin along the x-axis.
  2. Read the y-coordinate (vertical position) → y = 5 — Point A is 5 units up from the origin along the y-axis.
  3. Write the coordinates as (x, y) → (7, 5) — The coordinates of point A are (7, 5).
Easy§ 02

What are the coordinates of point A and point B?

Answer: A = (8, 4), B = (3, 4)

  1. Read the coordinates of point A → A = (8, 4) — Point A is at x = 8, y = 4.
  2. Read the coordinates of point B → B = (3, 4) — Point B is at x = 3, y = 4.
Medium§ 03

What is the distance between (4, 7) and (6, 7)?

Answer: 2

  1. Since y-coordinates are equal, subtract x-coordinates → |6 - 4| = 2 — For points on a horizontal line, distance = difference of x-coordinates.
§ 04

Common mistakes

  • Confusing the order of coordinates by writing (y, x) instead of (x, y) — for example, writing (5, 3) as the coordinates when the point is actually at (3, 5).
  • Reading coordinates from the wrong axis, such as stating that point (4, 7) is 7 units right and 4 units up, when it should be 4 units right and 7 units up.
  • Starting the count from 1 instead of 0 at the origin, leading to coordinates like (4, 3) being read as (5, 4) due to counting the origin as position 1.
§ 05

Frequently asked questions

What does the first quadrant mean in coordinates?
The first quadrant contains all points where both x and y coordinates are positive numbers. This means points are located to the right of and above the origin (0, 0). In school mathematics, pupils typically start with first quadrant coordinates before learning about negative coordinates in other quadrants.
How do you remember which coordinate comes first?
The x-coordinate always comes first in the pair (x, y). A helpful memory aid is 'along before up' — move along the horizontal x-axis first, then up the vertical y-axis. Some pupils remember 'x comes before y in the alphabet' to maintain the correct order.
What is the origin in coordinate geometry?
The origin is the point (0, 0) where the x-axis and y-axis meet. All coordinate measurements start from this central reference point. When reading coordinates, count the number of units right from the origin for x, and the number of units up from the origin for y.
Can coordinates have decimal values in the first quadrant?
Yes, coordinates can include decimal values like (2.5, 3.7) or (1.25, 4.8). These represent positions between the whole number grid lines. Decimal coordinates are particularly common in real-world applications where precise measurements are needed, such as GPS locations or engineering drawings.
How do you find the distance between two points with the same y-coordinate?
When two points share the same y-coordinate, they lie on a horizontal line. The distance equals the absolute difference between their x-coordinates. For points (3, 5) and (8, 5), the distance is |8 - 3| = 5 units. This method works because the points form a straight horizontal line.
§ 06

See also

Mean
§ 06

Where to next?

Prerequisites
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