🔵Plotting Points Using (x, y) - Both Positive
What is a Coordinate Plane?
A coordinate plane is a flat surface with two perpendicular number lines:
- x-axis (horizontal) → left to right
- y-axis (vertical) → up and down
The first quadrant is where both x and y are positive numbers.
Ordered Pairs (x, y):
- First number = x-coordinate (horizontal position)
- Second number = y-coordinate (vertical position)
- Always written as (x, y)
The Origin:
- Point where axes meet
- Coordinates: (0, 0)
COORDINATE PLANE - FIRST QUADRANT:
y-axis
↑
10 │
9 │
8 │
7 │
6 │
5 │
4 │
3 │
2 │
1 │
0 └──────────────────→ x-axis
0 1 2 3 4 5 6 7 8 9 10
PLOTTING POINT (4, 6):
Step 1: Start at origin (0,0)
Step 2: Move RIGHT 4 spaces on x-axis
Step 3: Move UP 6 spaces on y-axis
Step 4: Mark the point and label it (4, 6)
y-axis
↑
6 │ • (4,6)
5 │ ↑
4 │ │
3 │ │ Up 6
2 │ │
1 │ │
0 └───┬───┴───→ x-axis
0 4
← Right 4 →
PLOTTING MULTIPLE POINTS:
y-axis
↑
5 │ A(2,5) C(5,4)
4 │ • •
3 │ B(1,3)
2 │ •
1 │ D(4,1)
0 └───┬───┬───┬───┬───→ x-axis
0 1 2 3 4 5
A(2,5) = Right 2, Up 5
B(1,3) = Right 1, Up 3
C(5,4) = Right 5, Up 4
D(4,1) = Right 4, Up 1👀 See a worked example
Plot point A(3, 5) on the coordinate plane.
- x = 3 → move RIGHT 3 units from origin
- y = 5 → move UP 5 units
- Mark point and label A
What are the coordinates of a point that is 6 units right and 2 units up from origin?
- Right 6 → x = 6
- Up 2 → y = 2
- Answer: (6, 2)
Plot and label: P(0, 4), Q(4, 0), R(2, 2)
- P(0,4): x=0 (no move right), up 4 → on y-axis
- Q(4,0): right 4, y=0 (no move up) → on x-axis
- R(2,2): right 2, up 2
``` y 5│ 4│ P(0,4) R(2,2) 3│ • 2│ • 1│ • 0└─┬─┬─┬─┬─┬─ x 0 1 2 3 4 5 Q(4,0)• ```
🤖 Vidi's Key Points
- Coordinate plane has x-axis (horizontal) and y-axis (vertical)
- First quadrant: both x and y are positive
- Ordered pair = (x, y)
- Origin = (0, 0)
- "Walk to the right, then climb up"
🟢Reading Coordinates from a Map/Grid
Real-World Application
Maps use coordinate grids to show locations! Each location has a unique address (x, y).
How to Read a Grid Map:
- Find the horizontal position (column) = x-coordinate
- Find the vertical position (row) = y-coordinate
- Read as (x, y)
Grid Map Example:
y=5 │ │ │ │ │ │
y=4 │ │ 🏠│ │🏪│ │
y=3 │ │ │ │ │ │
y=2 │🏫│ │ │ │🏥│
y=1 │ │ │ │ │ │
└───┴───┴───┴───┴───┘
x=1 x=2 x=3 x=4 x=5
House (🏠) is at (2, 4)
School (🏫) is at (1, 2)
Store (🏪) is at (4, 4)
Hospital (🏥) is at (5, 2)TREASURE MAP COORDINATES:
y
10│
9│ 🌲(3,9)
8│
7│ 🏠(8,7)
6│ 💎(5,6)
5│ ⛵(1,5)
4│
3│ 🔑(7,3)
2│
1│ 🏴☠️(9,1)
0└──┬──┬──┬──┬──┬──┬──┬──┬──┬──→ x
0 1 2 3 4 5 6 7 8 9 10
⛵ Boat = (1,5)
💎 Diamond = (5,6)
🌲 Tree = (3,9)
🏠 House = (8,7)
🔑 Key = (7,3)
🏴☠️ Treasure = (9,1)
CLASSROOM SEATING CHART:
y=6 │ │ │ │ │
y=5 │ John│Lisa │Mark │ │
y=4 │ Anna│ │ │ │
y=3 │ │ │ Sam │ │
y=2 │ │ │ │ │
y=1 │ │ │ │ │
└─────┴─────┴─────┴─────┘
x=1 x=2 x=3 x=4
John's seat = (2, 5)
Lisa's seat = (3, 5)
Anna's seat = (1, 4)
Sam's seat = (3, 3)👀 See a worked example
On a zoo map, the lions are at (3, 7) and elephants at (8, 4). Which animal is more to the right?
- x-coordinate tells right/left position
- Lions: x=3, Elephants: x=8
- 8 > 3, so elephants are more to the right
- Answer: Elephants
A city grid has library at (2, 5) and park at (2, 2). What is the same about them?
- Both have x = 2
- Same x-coordinate means they are on the same vertical line
- Answer: Same x-coordinate (directly above/below each other)
On a coordinate grid, point P is at (4, 7). If you move left 2 and down 3, where do you end?
- Left 2: x = 4 - 2 = 2
- Down 3: y = 7 - 3 = 4
- Answer: (2, 4)
🤖 Vidi's Key Points
- Read coordinates as (x, y) → horizontal first, then vertical
- Same x = same vertical line
- Same y = same horizontal line
- Maps use coordinates to locate places
- Always start at origin when reading coordinates
🟣Horizontal & Vertical Distance Between Points
Finding Distance on a Coordinate Plane
Since we're only in the first quadrant, all coordinates are positive. Distances are always positive.
Horizontal Distance (Left to Right):
- Points have the same y-coordinate
- Distance = |x₂ - x₁|
Vertical Distance (Up and Down):
- Points have the same x-coordinate
- Distance = |y₂ - y₁|
Distance Formula for Same Row/Column:
Horizontal: |x₂ - x₁| Vertical: |y₂ - y₁|
Note: | | means "absolute value" (always positive)
HORIZONTAL DISTANCE (Same y):
y=5 A(2,5) B(7,5)
• ←─ 5 units ─→ •
Distance = |7 - 2| = 5 units
<---|---|---|---|---|--->
2 3 4 5 6 7
VERTICAL DISTANCE (Same x):
y=8 B(4,8)
•
↑
│ 3 units
↓
y=5 A(4,5)
•
Distance = |8 - 5| = 3 units
BOTH HORIZONTAL & VERTICAL (L-shaped path):
y=7 B(9,7)
•
↑
│ 4 units
↓
y=3 A(3,3) •
← 6 units → C(9,3)
•
Horizontal distance = 6 units
Vertical distance = 4 units
Total path (taxicab distance) = 6 + 4 = 10 units
FINDING DISTANCE - STEP BY STEP:
Points: P(2,8) and Q(2,3)
Step 1: Same x? YES (both x=2)
Step 2: Distance = |8 - 3| = 5 units
Points: R(1,4) and S(6,4)
Step 1: Same y? YES (both y=4)
Step 2: Distance = |6 - 1| = 5 units👀 See a worked example
Find the distance between A(3, 5) and B(8, 5).
- Same y-coordinate (y=5) → horizontal distance
- Distance = |8 - 3| = 5
- Answer: 5 units
Find the distance between C(2, 1) and D(2, 9).
- Same x-coordinate (x=2) → vertical distance
- Distance = |9 - 1| = 8
- Answer: 8 units
A bird is at (4, 6) and its nest is at (4, 2). How far must it fly straight down?
- Same x (both 4) → vertical
- Distance = |6 - 2| = 4
- Answer: 4 units
Two points: (5, 3) and (12, 3). What is the horizontal distance?
- Same y=3
- Distance = |12 - 5| = 7
- Answer: 7 units
🤖 Vidi's Key Points
- Same x → vertical distance (|y₂ - y₁|)
- Same y → horizontal distance (|x₂ - x₁|)
- Distance is always positive
- Units depend on grid scale
- To find L-shaped path: add horizontal + vertical
🎯 Mission Test
Ready, Maths Hero? Take the chapter test to show what you've learned!
Start the Chapter Test →