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.)
