The Coordinate Plane
The coordinate plane is a grid with two number lines: x (horizontal) and y (vertical) crossing at the origin (0,0). Every point has an address (x, y) called an ordered pair. It is the foundation of graphing, algebra, and eventually all of calculus.
Key Concepts
Quadrants and Plotting Points
The plane is divided into 4 quadrants. Quadrant I: (+,+). Quadrant II: (−,+). Quadrant III: (−,−). Quadrant IV: (+,−). To plot (3, −2): go right 3 on x-axis, then down 2 on y-axis. Always x first, then y.
Distance and Midpoint
Distance between two points on the same horizontal or vertical line: just subtract coordinates. (1,4) to (7,4) → |7−1| = 6 units. Midpoint: average the coordinates. Midpoint of (1,4) and (7,4) = ((1+7)/2, 4) = (4, 4).
Patterns and Graphing Rules
A rule like y = x + 2 creates a straight line. Make a table: x=0→y=2, x=1→y=3, x=2→y=4. Plot the points and connect them. The coordinate plane lets you see patterns in numbers as pictures.
🆕 Coordinate Plane
Click anywhere on the grid to plot a point. See its coordinates!
✅ Check Your Understanding
1. An ordered pair (x, y) — which coordinate comes first?
2. In which quadrant is the point (−3, 4)?
3. What is the midpoint between (2, 6) and (8, 6)?