On this page, we practice deciding whether a point lies in a quadrant, on an axis, or at the origin.
Remember
For a point \((x,y)\):
- \(Q1: ((+,+)\)
- \(Q2: ((-,+)\)
- \(Q3: ((-,-)\)
- \(Q4: ((+,-)\)
If one coordinate is zero, check whether the point lies on an axis.
If both coordinates are zero, the point is at the origin.
Example 1 – Quadrant 1
Determine where the point lies:
$$P=(4,3)$$
The \(x\)-coordinate is positive, and the \(y\)-coordinate is positive.
Therefore, the signs are:
$$(+,+)$$
So, the point is in \(Q1\).
Example 2 – Quadrant 2
Determine where the point lies:
$$P=(-5,2)$$
The \(x\)-coordinate is negative, and the \(y\)-coordinate is positive.
Therefore, the signs are:
$$(-,+)$$
So, the point is in \(Q2\).
Example 3 – Quadrant 3
Determine where the point lies:
$$P=(-2,-6)$$
The \(x\)-coordinate is negative, and the \(y\)-coordinate is negative.
Therefore, the signs are:
$$(-,-)$$
So, the point is in \(Q3\).
Example 4 – Quadrant 4
Determine where the point lies:
$$P=(3,-4)$$
The \(x\)-coordinate is positive, and the \(y\)-coordinate is negative.
Therefore, the signs are:
$$(+,-)$$
So, the point is in \(Q4\).
Example 5 – On the \(x\)-Axis
Determine where the point lies:
$$P=(-7,0)$$
The \(y\)-coordinate is zero.
Therefore, the point lies on the \(x\)-axis.
It is not in any quadrant.
Example 6 – On the \(y\)-Axis
Determine where the point lies:
$$P=(0,5)$$
The \(x\)-coordinate is zero.
Therefore, the point lies on the \(y\)-axis.
It is not in any quadrant.
Example 7 – At the Origin
Determine where the point lies:
$$P=(0,0)$$
Both coordinates are zero.
Therefore, the point is at the origin.
The origin lies on both axes and is not in any quadrant.
Practice
- More Examples (Current page)
- Take the Quiz
Continue Learning
- Plotting Points on the Coordinate Plane (\(2D\))
- Which Quadrant or Axis? Points on the Coordinate Plane \(2D\)
- Distance Formula in \(2D\)
- Distance between Two Points in \(2D\)
- Distance Formula: Radius and Area of a Circle