C3.1 Coordinates

Learning objectives

C3.1.1Use and interpret Cartesian coordinates in two dimensions.• Use and interpret Cartesian coordinates in two dimensions.

A Cartesian coordinate $(x,y)$ locates a point using two directed movements from the origin $(0,0)$ : move horizontally by $x$ , then vertically by $y$ .

Coordinate sign	Movement
$x>0$	right
$x<0$	left
$y>0$	up
$y<0$	down

To read a plotted point, project it to the horizontal $x$ -axis first and record that value; then project it to the vertical $y$ -axis and record the second value. For a point three units right and two units down, write $(3,-2)$ .

To plot $(-2,4)$ , start at the origin, move 2 units left to $x=-2$ , then 4 units up to $y=4$ . Mark the point only where these two coordinate lines meet.

Point location	Coordinate fact
on the $x$ -axis	$y=0$
on the $y$ -axis	$x=0$
at the origin	$x=0$ and $y=0$

Read the scale on each axis independently before counting grid spaces: one square may represent more than one unit, and the two axes can use different scales.

Coordinate order never changes: $(x,y)$ means horizontal first, vertical second. For example, $(-2,4)$ and $(4,-2)$ are different points.

Next Topic

—C3.2 Drawing linear graphsRead