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Door 15 · Grade 5

📐 Coordinate Plane (1st Quadrant)

Coordinate plane has x-axis (horizontal) and y-axis (vertical)

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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)

Worked example

Problem: Plot point A(3, 5) on the coordinate plane.

  1. x = 3 → move RIGHT 3 units from origin
  2. y = 5 → move UP 5 units
  3. Mark point and label A

Answer: Mark point and label A

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)

Worked example

Problem: On a zoo map, the lions are at (3, 7) and elephants at (8, 4). Which animal is more to the right?

  1. x-coordinate tells right/left position
  2. Lions: x=3, Elephants: x=8
  3. 8 > 3, so elephants are more to the right
  4. Answer: Elephants

Answer: Answer: Elephants

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)

Worked example

Problem: Find the distance between A(3, 5) and B(8, 5).

  1. Same y-coordinate (y=5) → horizontal distance
  2. Distance = |8 - 3| = 5
  3. Answer: 5 units

Answer: Answer: 5 units