E3.1 Coordinates

Learning objectives

E3.1.1Use and interpret Cartesian coordinates in two dimensions.• Use and interpret Cartesian coordinates in two dimensions.

A Cartesian coordinate $(x,y)$ records a point’s horizontal and vertical positions in that order. Accurate interpretation depends on order, sign and the scale of each axis.

Coordinate	Positive direction	Negative direction
$x$	right	left
$y$	up	down

To read a point, project to the $x$ -axis and then the $y$ -axis. To plot it, start at $(0,0)$ , move horizontally by $x$ , then vertically by $y$ . Read each axis scale independently before counting grid spaces.

Location	Coordinate condition
on the $x$ -axis	$y=0$
on the $y$ -axis	$x=0$
at the origin	$(0,0)$

Coordinates can also encode a shape. Compare corresponding coordinate changes: moving from $A(x_1,y_1)$ to $B(x_2,y_2)$ changes $x$ by $x_2-x_1$ and $y$ by $y_2-y_1$ . Apply the same changes to another vertex when equal, parallel sides require the same displacement.

$A(1,1),\ B(4,2),\ D(2,5):\quad C=B+(D-A)=(4,2)+(1,4)=(5,6)$

Check any inferred point against every stated condition: coordinate signs, whole-number restrictions, equal side movement, and the order in which vertices are named.

Do not swap coordinates or treat a shape sketch as accurately scaled. Derive positions from the grid values and stated geometric relationships.

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—E3.2 Drawing linear graphsRead