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

Answer:

Option B is correct

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

Step-by-step 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:

$BD = \sqrt{(1-(-1))^2+(-3-3)^2}$ or  $BD = \sqrt{(1+1)^2+(-6)^2}$

$BD = \sqrt{(2)^2+(-6)^2}$ or  $BD = \sqrt{4+36} = \sqrt{40}$

⇒ $BD = 2\sqrt{10}$ = $2 \cdot 3.16227766 = 6.32455532$

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