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

Option (1)

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 =
`√((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 =
`√((2+2)^2+(7-1)^2)`

AB =
`√(4^2+6^2)`

AB =
`√(52)`

AB =
`2√(13)`

Now area of square ABCD = 4 ×
`2√(13)`

=
`8√(13)` unit

Therefore, option (1) will be the answer.