Explanation
The coordinate plane is divided into four regions called quadrants.
The horizontal \(x\)-axis and the vertical \(y\)-axis divide the coordinate plane into these four quadrants.
We can determine where a point \((x,y)\) is located by looking at the signs of its \(x\)- and \(y\)-coordinates.
A point may be:
- in one of the four quadrants
- on the \(x\)-axis
- on the \(y\)-axis
- at the origin \((0,0)\)
Points on an axis are not in any quadrant.
The origin \((0,0)\) lies on both the \(x\)-axis and the \(y\)-axis and is not in any quadrant.
Formula / Rule
For a point:
$$(x,y)$$
use the following rules:
- \(Q1: (+,+)\)
- \(Q2: (-,+)\)
- \(Q3: (-,-)\)
- \(Q4: (+,-)\)
Also remember:
- If \(y=0\) and \(x\neq0\), the point is on the \(x\)-axis.
- If \(x=0\) and \(y\neq0\), the point is on the \(y\)-axis.
- If \(x=0\) and \(y=0\), the point is at the origin.
So, always check for a zero coordinate before deciding which quadrant contains the point.
Example
Determine which quadrant or axis contains the point:
$$P=(-3,4)$$
The \(x\)-coordinate is negative:
$$x=-3<0$$
The y-coordinate is positive:
$$y=4>0$$
A point with signs:
$$(-,+)$$
lies in Quadrant \(2\).
Therefore:
$$P=(-3,4)$$
is in \(Q2\).
Video Explanation
Practice
Continue Learning
- Plotting Points on the Coordinate Plane (\(2D\))
- Which Quadrant or Axis? Points on the Coordinate Plane \(2D\) (Current lesson)
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- Distance between Two Points in \(2D\)
- Distance Formula: Radius and Area of a Circle