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
and
is,
d = ![\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
Therefore, distance between two points A(-2, 1) and B(2, 7) will be,
AB = ![\sqrt{(2+2)^2+(7-1)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%282%2B2%29%5E2%2B%287-1%29%5E2%7D)
AB = ![\sqrt{4^2+6^2}](https://tex.z-dn.net/?f=%5Csqrt%7B4%5E2%2B6%5E2%7D)
AB = ![\sqrt{52}](https://tex.z-dn.net/?f=%5Csqrt%7B52%7D)
AB = ![2\sqrt{13}](https://tex.z-dn.net/?f=2%5Csqrt%7B13%7D)
Now area of square ABCD = 4 × ![2\sqrt{13}](https://tex.z-dn.net/?f=2%5Csqrt%7B13%7D)
=
unit
Therefore, option (1) will be the answer.