Coordinate Plane

Axes and origin

The axes meet at the origin $(0,0)$. Positive $x$-values lie to the right and negative $x$-values to the left. Positive $y$-values lie above the origin and negative $y$-values below it.

The scale must be read before plotting. One grid square might represent $1$, $5$, $0.5$, or another interval.

Ordered pairs

Coordinates are ordered: move horizontally using $x$, then vertically using $y$. The points $(3,-2)$ and $(-2,3)$ are different.

A point on the $x$-axis has $y=0$. A point on the $y$-axis has $x=0$.

Graphing relationships

A graph turns pairs of related values into a visual pattern. If $y=2x+1$, substitute chosen $x$-values to create points such as $(0,1)$, $(1,3)$, and $(2,5)$. Their alignment reveals a linear relationship.

Not every context should connect points with a continuous line. A graph of ticket count may use separate points because fractional tickets are impossible.

Transformations

Coordinates describe geometric movement precisely. Adding $3$ to every $x$-coordinate translates a figure right $3$ units. Negating every $x$-coordinate reflects it across the $y$-axis. These rules connect coordinate geometry with function transformations.

Common mistakes

Reversing coordinates. Read and plot $x$ before $y$.

Ignoring the scale. Check labelled ticks instead of assuming one square equals one unit.

Misnumbering quadrants. Begin in the upper right and move counterclockwise.

Dropping negative signs in differences. Use brackets when substituting negative coordinates into formulas.

Quick self-check

• What does each grid interval represent?
• Did I move horizontally before vertically?
• Do the coordinate signs match the point’s region?
• Does the context justify connecting plotted points?