Quadrants
In short: Quadrants are the four regions that the x-axis and y-axis cut the coordinate plane into, numbered I to IV counterclockwise starting at the upper right.
6th GradeGeometry6.NS.C.6b
What is Quadrants?
The two axes act like a plus sign and split the plane into four quadrants. Each region is a corner of the plane where the signs of x and y never change, so the signs tell you the region at once.
Precisely, Quadrant I has \(x > 0, y > 0\); Quadrant II has \(x < 0, y > 0\); Quadrant III has \(x < 0, y < 0\); and Quadrant IV has \(x > 0, y < 0\). Points on an axis, such as \((0, 5)\), belong to no quadrant.
How to spot it
- A problem asks “in which quadrant” a point lies, or which quadrant has only negative coordinates.
- A reflection over an axis moves a figure into a neighboring region.
- A graph of real-life data uses only positive values, so everything sits in the upper right.
- A point has a zero coordinate and you must decide whether it belongs to any region.
The method
- Read the pair \((x, y)\) and note the sign of each number.
- Positive x means right of the y-axis; positive y means above the x-axis.
- Match the two signs: (+, +) is I, (-, +) is II, (-, -) is III and (+, -) is IV.
- If either coordinate is 0, report that the point is on an axis.
Quadrants: solved example
Problem
A drone pilot logs positions as (east-west, north-south) in yards from a launch pad. Name the quadrant of \((-48, 15)\), \((20, -7)\) and \((-5, -90)\).
Solution
\((-48, 15)\): x negative, y positive, so Quadrant II.
\((20, -7)\): x positive, y negative, so Quadrant IV. \((-5, -90)\): both negative, so Quadrant III.
Try it
Question 1
The point \((6, 9)\) is reflected across the y-axis. In which quadrant is the image?
Show the answer
The image is \((-6, 9)\): x negative and y positive, so Quadrant II.
Question 2
Which quadrant contains no points whose coordinates are both positive?
Show the answer
Quadrants II, III and IV contain none; only Quadrant I has both coordinates positive.
Quadrants vs. Coordinate Plane
A quadrant is one of four pieces. The coordinate plane is the whole surface, including its axes. A point on an axis is part of the plane but not part of any quadrant.
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Whole dictionary: A–Z · 6th Grade · Geometry