Skill: Plot points in all four quadrants

The 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, $((0,0))$.

To plot an ordered pair $((x,y))$:

1. Start at the origin.
2. Move horizontally according to $x$: right if $x$ is positive and left if $x$ is negative.
3. Move vertically according to $y$: up if $y$ is positive and down if $y$ is negative.
4. Mark and label the point.

The quadrants have these sign patterns:

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

Example

Plot the points

$$A(3,2),\qquad B(-4,1),\qquad C(-2,-3),\qquad D(1,-4).$$

Point $(A(3,2))$:

• The $x$-coordinate is $3$, so move $3$ units right.
• The $y$-coordinate is $2$, so move $2$ units up.
• $A$ is in Quadrant I.

Point $(B(-4,1))$:

• The $x$-coordinate is $(-4)$, so move $4$ units left.
• The $y$-coordinate is $1$, so move $1$ unit up.
• $B$ is in Quadrant II.

Point $(C(-2,-3))$:

• The $x$-coordinate is $(-2)$, so move $2$ units left.
• The $y$-coordinate is $(-3)$, so move $3$ units down.
• $C$ is in Quadrant III.

Point $(D(1,-4))$:

• The $x$-coordinate is $1$, so move $1$ unit right.
• The $y$-coordinate is $(-4)$, so move $4$ units down.
• $D$ is in Quadrant IV.

Always read the coordinates in order: $x$ first, then $y$. If one coordinate is $0$, the point lies on an axis rather than in a quadrant.