Option C : The perimeter is 13.3 units
Explanation:
The coordinates of the given shape is [tex]J(-3,4), K(-1,6), L(1,1)[/tex] and [tex]\mathrm{M}(-1,3)[/tex]
To determine the perimeter, first let us find the lengths of the sides using the distance formula,
[tex]d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}[/tex]
The length of JK is given by
[tex]\begin{aligned}J K &=\sqrt{(-1+3)^{2}+(6-4)^{2}} \\&=\sqrt{2^{2}+2^{2}} \\&=\sqrt{4+4} \\&=\sqrt{8}\end{aligned}[/tex]
The length of KL is given by
[tex]\begin{aligned}K L &=\sqrt{(1+1)^{2}+(1-6)^{2}} \\&=\sqrt{2^{2}+(-5)^{2}} \\&=\sqrt{4+25} \\&=\sqrt{29}\end{aligned}[/tex]
The length of LM is given by
[tex]\begin{aligned}L M &=\sqrt{(-1-1)^{2}+(3-1)^{2}} \\&=\sqrt{(-2)^{2}+(2)^{2}} \\&=\sqrt{4+4} \\&=\sqrt{8}\end{aligned}[/tex]
The length of JM is given by
[tex]\begin{aligned}J M &=\sqrt{(-1+3)^{2}+(3-4)^{2}} \\&=\sqrt{(2)^{2}+(-1)^{2}} \\&=\sqrt{4+1} \\&=\sqrt{5}\end{aligned}[/tex]
The perimeter of the given shape is
[tex]Perimeter = \ JK \ + \ KL \ + \ LM \ + \ JM[/tex]
[tex]Perimeter = \ \sqrt{8} \ + \ \sqrt{29} \ + \sqrt{8} \ + \sqrt{5}[/tex]
[tex]Perimeter=13.278[/tex]
[tex]Perimeter=13.3 \ units[/tex]
Hence, the perimeter is 13.3 units
Thus, Option C is the correct answer.
