Respuesta :
Answer:
The correct option is 4. The perimeter of ABCD is 19.1.
Step-by-step explanation:
The coordinates of shape are A(-3,5), B(2,6), C(0,2), D(-5,1).
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The length of all sides are
[tex]AB=\sqrt{(2-(-3))^2+(6-5)^2}=\sqrt{25+1}= \sqrt{26}[/tex]
[tex]BC=\sqrt{(0-2)^2+(2-6)^2}=\sqrt{4+16}= \sqrt{20}[/tex]
[tex]CD=\sqrt{(-5-0)^2+(1-2)^2}=\sqrt{25+1}= \sqrt{26}[/tex]
[tex]AD=\sqrt{(-5-(-3))^2+(1-5)^2}=\sqrt{4+16}= \sqrt{20}[/tex]
The perimeter of ABCD is
[tex]P=\sqrt{26}+\sqrt{20}+\sqrt{26}+\sqrt{20}[/tex]
[tex]P=2(\sqrt{26}+\sqrt{20})[/tex]
[tex]P=19.14231[/tex]
[tex]P\approx 19.1[/tex]
The perimeter of ABCD is 19.1. Therefore correct option is 4.
