Question

Examine the diagram and information to answer the question. Square ABCD has vertices at A(−2,1), B(2,7), C(8,3), and D(4,−3). How many units is the perimeter of square ABCD?

Answer 1

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 $(x_1,y_1)$ and $(x_2,y_2)$ is,

d = $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Therefore, distance between two points A(-2, 1) and B(2, 7) will be,

AB = $\sqrt{(2+2)^2+(7-1)^2}$

AB = $\sqrt{4^2+6^2}$

AB = $\sqrt{52}$

AB = $2\sqrt{13}$

Now area of  square ABCD = 4 × $2\sqrt{13}$

                                              = $8\sqrt{13}$ unit

Therefore, option (1) will be the answer.