📖Definition
The coordinate plane (also called the Cartesian plane) is a two-dimensional surface formed by two perpendicular number lines: the horizontal x-axis and vertical y-axis. Points are located using ordered pairs (x, y) where x is the horizontal position and y is the vertical position.
📐Formula
In an ordered pair (x, y): x tells you how far to move left/right from the origin, y tells you how far to move up/down. The origin (0, 0) is where the axes cross.
📝Step-by-Step Guide
Understand the Axes
The x-axis is horizontal (left-right), the y-axis is vertical (up-down). They meet at the origin (0, 0).
Know the Quadrants
Quadrant I: (+, +), Quadrant II: (-, +), Quadrant III: (-, -), Quadrant IV: (+, -).
Plot a Point
Start at origin, move horizontally by the x-value, then vertically by the y-value.
Find Distance Between Points
Use the distance formula derived from the Pythagorean theorem.
⚠️Common Mistakes to Avoid
- Writing (y, x) instead of (x, y)
- Moving vertically first instead of horizontally
- Confusing which quadrant has which signs
- Forgetting that the origin is (0, 0)
- Mixing up positive and negative directions
✏️Practice Problems
In which quadrant is the point (-3, 5)?
Answer: Quadrant II
Find the distance between (0, 0) and (3, 4)
Answer: 5 units
Find the distance between (-2, 3) and (4, -5)
Answer: 10 units
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