Question

Find the length of a diagonal of a rectangle ABCD with vertices A(-3,1), B(-1,3), C(3,1), and D(1,-3). (1 point)

A. 5.7
B. 6.3
C. 3.2
D. 4.5

Answer 1

The length of diagonal will be 6.3
we can do this by using distance formula and points B(-1,3) and D1,-3)

Answer 2

Option B is correct

The length of a diagonal of a rectangle is, 6.3 (approx)

Explanation:

Given: The rectangle ABCD with vertices A(-3 , 1) , B(-1 ,3) , C(3,1) and D(1 , -3).

Use Distance formula to calculate the diagonal of Rectangle:

Distance formula for any two points is given by:

`D= \sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2}`

In this rectangle ABCD, the two diagonals are equal in length and bisect each other, i.e, length of BD and length of AC are equal .

therefore, using distance formula to find the length of BD:

here, coordinates are B(-1 , 3) and D(1 ,-3)

then:

`BD = √((1-(-1))^2+(-3-3)^2)` or
`BD = √((1+1)^2+(-6)^2)`

`BD = √((2)^2+(-6)^2)` or
`BD = √(4+36) = √(40)`

⇒
`BD = 2√(10)` =
`2 \cdot 3.16227766 = 6.32455532`

Therefore, the length of a diagonal of a Rectangle is, 6.3 (approx.)