## The Cartesian Coordinate System

7.3  The Cartesian Coordinate System

 Example The following diagram shows that $$EFGH$$ is a rectangle drawn on a Cartesian plane. $$M$$ is the midpoint of $$EH.$$  State the coordinate of $$G$$. Given that midpoint $$EH$$ is $$M(8,6)$$. \begin{aligned} (8,6)&= (\dfrac {2+x} {2} , \dfrac{6+y}{2}) \end{aligned} \begin{aligned} 8&= \dfrac {2+x} {2} \\\\16&=2+x \\\\x&= 14. \end{aligned} \begin{aligned} 6&= \dfrac {6+y} {2} \\\\12&=6+y \\\\y&= 6. \end{aligned} So, $$H= (14,6)$$. Noted that, $$EH$$ is parallel to $$FG$$ and $$x$$-axis.  So, the $$x$$-coordinate of $$G$$ is $$14$$, while the $$y$$-coordinate of $$G$$ is $$3$$. Thus, $$G = (14, 3).$$

## The Cartesian Coordinate System

7.3  The Cartesian Coordinate System

 Example The following diagram shows that $$EFGH$$ is a rectangle drawn on a Cartesian plane. $$M$$ is the midpoint of $$EH.$$  State the coordinate of $$G$$. Given that midpoint $$EH$$ is $$M(8,6)$$. \begin{aligned} (8,6)&= (\dfrac {2+x} {2} , \dfrac{6+y}{2}) \end{aligned} \begin{aligned} 8&= \dfrac {2+x} {2} \\\\16&=2+x \\\\x&= 14. \end{aligned} \begin{aligned} 6&= \dfrac {6+y} {2} \\\\12&=6+y \\\\y&= 6. \end{aligned} So, $$H= (14,6)$$. Noted that, $$EH$$ is parallel to $$FG$$ and $$x$$-axis.  So, the $$x$$-coordinate of $$G$$ is $$14$$, while the $$y$$-coordinate of $$G$$ is $$3$$. Thus, $$G = (14, 3).$$