Solution :
GIven, a rectangle ABCD with vertices A (-3,1) B(-1,3) C (3,-1)
To Calculate the Diagonal, first calculate the length and width of the rectangle.
Length and width of a rectange ABCD are
AB=[tex]\sqrt{(-1-(-3))^2 + (3-1)^2}=\sqrt{2^2+2^2}=2\sqrt{2}[/tex]
BC=[tex] \sqrt{(3-(-1))^2+(-1-3)^2} = \sqrt{4^2+(-4)^2}=4\sqrt{2} [/tex]
Length and width of rectangle ABCD are [tex] 4\sqrt{2} , 2\sqrt{2} [/tex].
Diagonal of the rectangle ABCD =
[tex] \sqrt{(4\sqrt{2})^2+(2\sqrt{2})^2} \\\\=\sqrt{32+8} \\\\=\sqrt{40}\\\\=2\sqrt{10} \\\\=6.3 [/tex]
Hence, the length of a diagonal of a rectangle ABCD with vertices A (-3,1) B(-1,3) C (3,-1) is 6.3
