Coordinates · Grade 6
In Grade 6 you learn: all four quadrants, midpoints, and coordinates in geometry problems.
Coordinates give the exact position of a point on a grid: (x, y) means x across and y up from the origin. With negative numbers the grid extends into four quadrants, and simple rules find midpoints and lengths of horizontal or vertical lines.
Key facts
- Write (x, y): across first, then up. “Along the corridor, then up the stairs.”
- Negative x is left of the origin; negative y is below it.
- Quadrants: first (+, +), second (−, +), third (−, −), fourth (+, −).
- The midpoint of (x₁, y₁) and (x₂, y₂) is ((x₁ + x₂)/2, (y₁ + y₂)/2).
- All points on the line x = a have x-coordinate a (a vertical line); y = b is horizontal.
Worked examples
Example 1
What are the coordinates of A and B?
Answer: A(3, 2), B(−2, −3)
Example 2
Find the midpoint of (−4, 7) and (6, 1).
Answer: (1, 4)
Example 3
M(2, −1) is the midpoint of AB, and A is (−3, 4). Find B.
Answer: B(7, −6)