Quick Notes

Quick Notes

Mathematics Chapter 7: Coordinates
7.3 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, \(G = (14, 3).\)