You the points A(-3, 5), B(1, 7), C(3, 3) and D(-1, 1).
You use the formula: AB= [tex] \sqrt{ ( x_{B}- x_{A} )^{2} +( y_{B}- y_{A} )^{2}} [/tex]
AB = [tex] \sqrt{ (-3-1)^{2} + (7-5)^{2} } = \sqrt{ 4^{2} + 2^{2} } = \sqrt{20} [/tex]
DC = [tex] \sqrt{ (3+1)^{2}+ (3-1)^{2} } = \sqrt{20} [/tex]
BC = [tex] \sqrt{ (1-3)^{2}+ (7-3)^{2} } = \sqrt{20} [/tex]
AD = [tex] \sqrt{ (-3+1)^{2}+(5-1)^{2} }= \sqrt{20} [/tex]
AB=DC and AD=BC => the shape is a parallelogram(1)
But AB=DC=AD=BC + (1) => the shape is a square
Perimeter for a square = 4*l =4* [tex] \sqrt{20} [/tex]
[tex] \sqrt{20} [/tex] = 4.472135
P=4*4.472135=17.8854 which is rounded to 17.9
The right answer is C. 17.9
