Question

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 1

B 12.68

Explanation:

you will need to find the distance between each segment-

so the length of DC, CF, FE, ED

`d=\sqrt{(x_(2)-x_(1)) ^(2)+(y_(2)-y_(1)) ^(2) }`

DC:

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

`d=\sqrt{(-1--2)^(2) +(2--1)^(2) } \\d=\sqrt{1^(2)+3^(2) } \\d=√(10) =3.16`

CF:

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

`d=\sqrt{(1--1)^(2) +(1-2)^(2) } \\d=\sqrt{2^(2)+-1^(2) } \\d=√(4+1) \\d=√(x) 5=2.24`

FE

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

`d=\sqrt{(2-1)^(2) +(-2-1)^(2) } \\d=\sqrt{1^(2) +(-3)^(2) } \\d=√(1+9) \\d=√(10)= 3.16`

ED

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

`d=\sqrt{(-2-2)^(2) +(-1--2)^(2) } \\d=\sqrt{(-4)^(2)+1^(2) } \\d=√(16+1) \\d=√(17)= 4.12\\`

3.16+2.24+3.16+4.12= 12.68