Coordinate Geometry

A coordinate plane is a grid formed by two number lines that intersect at their zero point, called the origin. The origin has coordinates \((0,0)\).

• The horizontal number line is called the \(x\)-axis.
• The vertical number line is called the \(y\)-axis.

The coordinates of a point are a pair of numbers, written as \((x, y)\), where \(x\) is the \(x\)-coordinate and \(y\) is the \(y\)-coordinate:

• The \(x\)-coordinate indicates the horizontal position along the \(x\)-axis, with positive numbers to the right of the origin and negative numbers to the left.
• The \(y\)-coordinate indicates the vertical position along the \(y\)-axis, with positive numbers above the origin and negative numbers below.

For example, the point \((-2,1)\) has \(x=-2\) (two units to the left) and \(y=1\) (one unit up).

Plot these points on a coordinate plane:$$A(-2,3),\quad B(3,-1),\quad \text{and}\quad C(-3,-2).$$

A table of points lists the coordinates of several points in a coordinate plane.

• The first row represents the \(x\)-coordinates.
• The second row represents the \(y\)-coordinates.

Each column of the table gives the coordinates of one point: the number in the first row is its \(x\)-coordinate, and the number in the second row is its \(y\)-coordinate.

\(\textcolor{colordef}{x}\)	\(\textcolor{colordef}{-2}\)	\(\textcolor{colordef}{1}\)	\(\textcolor{colordef}{2}\)
\(\textcolor{colorprop}{y}\)	\(\textcolor{colorprop}{-3}\)	\(\textcolor{colorprop}{3}\)	\(\textcolor{colorprop}{-1}\)

This table represents the points \((\textcolor{colordef}{-2},\textcolor{colorprop}{-3}), (\textcolor{colordef}{1},\textcolor{colorprop}{3}), (\textcolor{colordef}{2},\textcolor{colorprop}{-1})\) on the coordinate plane: