Definition: A quadrant is one of the four regions into which the x-axis and y-axis divide the coordinate plane, numbered I to IV counterclockwise starting at the upper right.
What are the quadrants?
The two axes slice the plane into four regions. Quadrant I is upper right, Quadrant II is upper left, Quadrant III is lower left, and Quadrant IV is lower right. They are numbered counterclockwise.
How do signs tell you the quadrant?
Check the signs of the coordinates:
- Quadrant I: (+, +)
- Quadrant II: (-, +)
- Quadrant III: (-, -)
- Quadrant IV: (+, -)
The point (-6, 9) has a negative x and a positive y, so it lies in Quadrant II.
What about points on the axes?
A point with a zero coordinate, like (0, 5) or (-3, 0), lies on an axis. It belongs to no quadrant.
How do reflections change the quadrant?
Reflecting (4, 7) across the y-axis changes the sign of x only, giving (-4, 7), which moves from Quadrant I to Quadrant II. Reflecting across the x-axis changes the sign of y instead.
What is a common error?
Numbering the quadrants clockwise. Always go counterclockwise from the upper right.