Question

The coordinates of quadrilateral JKLM are J (1,3), K(3, 1), L (-1, -3) and M(-3,-1). What is the perimeter of quadrilateral JKLM?

Answer 1

the coodrinates of JKLM is,

J(1,3) , K(3,1), L(-1,-3) and M(-3,-1)

the length JK is ,

`\begin{gathered} JK=\sqrt[]{(1-3)^2+(3-1)^2} \\ =\sqrt[]{4+4} \\ =\sqrt[]{8} \\ =2\sqrt[]{2} \end{gathered}`

length KL is,

`\begin{gathered} KL=\sqrt[]{(-3-1)^2+(-1-3)^2} \\ =\sqrt[]{16+16} \\ =\sqrt[]{32} \\ =4\sqrt[]{2} \end{gathered}`

Length LM is,

`LM=\sqrt[]{(-3-(-1))^2+(-1-(-3))^2}`
`\begin{gathered} LM=\sqrt[]{4+4} \\ LM=2\sqrt[]{2} \end{gathered}`

length MJ

`\sqrt[]{(-1-3)^2+(-3-1)^2}`
`\begin{gathered} MJ=\sqrt[]{16+16} \\ MJ=4\sqrt[]{2} \end{gathered}`

so, the perimeter = sum of sides,

= JK + KL + LM + MJ

= 2 root 2 + 4root2 + 2root2 + 4root2

= 12 root 2

thus, the perimeter is 12 root 2