Find the perimeter of a quadrilateral with vertices at C (-1, 2), D (-2, -1), E (2, -2), and F (1, 1). Round your answer to the nearest hundredth when necessary.

A. 10.92 units
B. 12.68 units
C. 13.43 units
D. 18.27 units

Answer:

B 12.68

Step-by-step explanation:

you will need to find the distance between each segment-

so the length of DC, CF, FE, ED

[tex]d=\sqrt{(x_{2}-x_{1}) ^{2}+(y_{2}-y_{1}) ^{2} }[/tex]

DC:

D(-2,-1) C(-1,2)

[tex]d=\sqrt{(-1--2)^{2} +(2--1)^{2} } \\d=\sqrt{1^{2}+3^{2} } \\d=\sqrt{10} =3.16[/tex]

CF:

C(-1,2) F(1,1)

[tex]d=\sqrt{(1--1)^{2} +(1-2)^{2} } \\d=\sqrt{2^{2}+-1^{2} } \\d=\sqrt{4+1} \\d=\sqrt{x} 5=2.24[/tex]

FE

F(1,1) E(2,-2)

[tex]d=\sqrt{(2-1)^{2} +(-2-1)^{2} } \\d=\sqrt{1^{2} +(-3)^{2} } \\d=\sqrt{1+9} \\d=\sqrt{10}= 3.16[/tex]

ED

E(2,-2) D(-2,-1)

[tex]d=\sqrt{(-2-2)^{2} +(-1--2)^{2} } \\d=\sqrt{(-4)^{2}+1^{2} } \\d=\sqrt{16+1} \\d=\sqrt{17}= 4.12\\[/tex]

3.16+2.24+3.16+4.12= 12.68

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