Locate points in all four quadrants

The coordinate plane consists of perpendicular horizontal and vertical axes, and an ordered pair $(x,y)$ locates a point by its horizontal position $x$ followed by its vertical position $y$ . For integer coordinates, the signs identify the quadrants: I $(+,+)$ , II $(-,+)$ , III $(-,-)$ , and IV $(+,-)$ ; a zero coordinate places a point on an axis rather than in a quadrant. This understanding supports later graphing of relationships and is limited here to integer-coordinate location, not general equations or transformations.

Detailed Explanation: Locate points in all four quadrants

A coordinate plane has two perpendicular number lines:

The horizontal axis is the $x$ -axis.
The vertical axis is the $y$ -axis.
They meet at the origin, $(0,0)$ .

An ordered pair is written as $(x,y)$ . Always move left or right first using $x$ , then up or down using $y$ .

The signs tell you the quadrant:

\begin{array}{c|c} \text{Quadrant} & \text{Signs of }(x,y)\\ \hline \text{I} & (+,+)\\ \text{II} & (-,+)\\ \text{III} & (-,-)\\ \text{IV} & (+,-) \end{array}

Example: Locate the point $(-3,2)$

The $x$ -coordinate is $-3$ . Start at the origin and move 3 units left.
The $y$ -coordinate is $2$ . From there, move 2 units up.
The point is $(-3,2)$ .
Its signs are $(-,+)$ , so it is in Quadrant II.

Remember: if a coordinate is $0$ , the point is on an axis, not in a quadrant. For example, $(0,4)$ is on the $y$ -axis, and $(-2,0)$ is on the $x$ -axis.

Learn by doing: Locate points in all four quadrants

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Cartesian Grid - Points

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