Functional Skills Level 2 — Geometry and Measures

2D Coordinates

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Reading and Plotting Coordinates
Coordinates: (x, y) — always x first, then y. "Along the corridor, then up the stairs."

Every point on a grid is described by two numbers in brackets: \((x, y)\). The first number (x) tells you how far to go right along the horizontal axis. The second number (y) tells you how far to go up the vertical axis.

First Quadrant — Plotting and Reading Points x y 0 1 2 3 4 5 6 0 1 2 3 4 5 A(1,2) B(3,5) C(5,1) D(4,4) Remember: Corridor First, Stairs Second CORRIDOR (x) go along x first STAIRS (y) then up y second Point Start: Origin (0,0)

Example 1 — Read the coordinates of point A at (3, 5)

Step 1
Start at the origin (0, 0) — where the two axes cross.
Step 2
Count 3 units right along the x-axis (horizontal). This gives x = 3.
Step 3
Count 5 units up the y-axis (vertical). This gives y = 5.
Step 4
Write the coordinates: (3, 5) — x always first, y always second.

Example 2 — Plot the point (4, 2) on a coordinate grid

Step 1
Start at the origin (0, 0).
Step 2
Move 4 units right along the x-axis.
Step 3
From that point, move 2 units up parallel to the y-axis.
Step 4
Mark the point with a cross and label it (4, 2).
Memory tip: Always write (x, y) — x comes first. Remember: corridor first, stairs second.
Common mistake: Reading (y, x) instead of (x, y). The horizontal axis is ALWAYS x and comes first in the coordinate pair.
✓ Quick Check 1 — Reading and Plotting Coordinates (First Quadrant)
Question 1 of 10
All Four Quadrants: Positive and Negative Coordinates
Quadrant I: (+,+)    Quadrant II: (−,+)    Quadrant III: (−,−)    Quadrant IV: (+,−)

The axes extend in both directions, creating four quadrants. Negative x means left of the origin; negative y means below the origin.

All Four Quadrants x y -4 -3 -2 -1 1 2 3 4 4 3 2 1 -1 -2 -3 -4 Q I Q II Q III Q IV P(3,4) Q(-2,3) R(-3,-2) S(2,-4) Negative Coordinates — Direction Guide 0 − + LEFT RIGHT x-axis (horizontal) 0 + UP − DOWN y-axis Point (−2, 3): go LEFT 2, then UP 3 x=−2 (left of origin) & y=3 (above origin) → Quadrant II

Example 1 — Plot and name the quadrant for (−3, 4)

Step 1
x = −3: move 3 units left of the origin along the x-axis.
Step 2
y = 4: move 4 units up from that position.
Step 3
Negative x and positive y → Quadrant II.

Example 2 — Write the coordinates of a point 2 left and 5 down from the origin

Step 1
2 left → x = −2 (negative because it is left of the origin).
Step 2
5 down → y = −5 (negative because it is below the origin).
Step 3
Coordinates = (−2, −5). Both negative → Quadrant III.
The four quadrants: Q1 (right and up, both +), Q2 (left and up, −x, +y), Q3 (left and down, both −), Q4 (right and down, +x, −y).
Negative coordinates: (−3, 4) is NOT the same as (3, 4). The minus sign means left (for x) or down (for y).
✓ Quick Check 2 — All Four Quadrants and Negative Coordinates
Question 1 of 10
Finding the midpoint and distance between two points is not required for FS2 Level 2.
Midpoint of A(1,2) and B(5,6) 0 1 2 3 4 5 0 1 2 3 4 5 A(1,2) B(5,6) M(3,4) Δx = 4 Δy = 4 Midpoint: (1+5)/2 = 3 (2+6)/2 = 4 M = (3, 4) Real Life: GPS Distance and Meeting Point Home (2, 3) School (6, 7) Midpoint (4,5) Δx=4 Δy=4 Distance: d=√((6-2)²+(7-3)²) =√(16+16) =√32 ≈ 5.66 units

Example 1 — Find the midpoint of A(1, 2) and B(5, 6)

Step 1
Average the x-coordinates: \(\dfrac{1+5}{2} = \dfrac{6}{2} = 3\)
Step 2
Average the y-coordinates: \(\dfrac{2+6}{2} = \dfrac{8}{2} = 4\)
Step 3
Midpoint M = (3, 4)

Example 2 — Find the distance between P(1, 1) and Q(4, 5)

Step 1
Horizontal difference: \(\Delta x = 4 - 1 = 3\)
Step 2
Vertical difference: \(\Delta y = 5 - 1 = 4\)
Step 3
Apply Pythagoras: \(\sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25}\)
Step 4
Distance = 5 units

Practice: 2D Coordinates Practice

Answer each question, then click Check All to see how you did.

#QuestionAnswerResult
11. Plot (2, 3): which quadrant?
22. A point is 4 right and 1 up from origin. Its coordinates?
33. Which quadrant is (−1, 5)?
44. Which quadrant is (3, −2)?
55. A point is 5 left and 2 up from origin. Write its coordinates.
66. Which quadrant is (−4, −1)?
77. A point is on the x-axis, 3 units right. Write its coordinates.
88. Which quadrant is (6, −3)?
99. Which quadrant is (−2, −6)?
1010. A point is 6 left and 2 down from origin. Write its coordinates.

⚠ Things to Watch Out For

  • Reading (x, y) in wrong order: Coordinates are ALWAYS (x, y) — horizontal first, vertical second. x tells you how far RIGHT (or left), y tells you how far UP (or down).
  • Confusing negative quadrants: Bottom-left quadrant: both negative (−,−). Top-left: (−,+). Bottom-right: (+,−). Top-right: (+,+). Sketch the axes to orient yourself.
  • Plotting (3, 5) as (5, 3): Go along the x-axis FIRST (3 right), then up the y-axis (5 up). Reversing plots a completely different point.
  • Negative coordinates — going the wrong direction: (−3, 4) means 3 LEFT on the x-axis, then 4 UP on the y-axis. Don't go right for negative x.
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