Answer:
Option (1)
Step-by-step explanation:
Coordinates of the vertices are A(-2, 1), B(2, 7), C(8, 3) and D(4, -3)
Since ABCD is a square,
Perimeter of a square = 4 × (length of a side)
= 4 × (AB)
Formula to calculate the distance between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is,
d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Therefore, distance between two points A(-2, 1) and B(2, 7) will be,
AB = [tex]\sqrt{(2+2)^2+(7-1)^2}[/tex]
AB = [tex]\sqrt{4^2+6^2}[/tex]
AB = [tex]\sqrt{52}[/tex]
AB = [tex]2\sqrt{13}[/tex]
Now area of square ABCD = 4 × [tex]2\sqrt{13}[/tex]
= [tex]8\sqrt{13}[/tex] unit
Therefore, option (1) will be the answer.
