Solve problems involving the Cartesian coordinate system

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, \(G = (14, 3).\)