Question

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

Answer 1

it is b (-1,3) the length of the rectangle

Answer 2

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=
`√((-1-(-3))^2 + (3-1)^2)=√(2^2+2^2)=2√(2)`

BC=
`√((3-(-1))^2+(-1-3)^2) = √(4^2+(-4)^2)=4√(2)`

Length and width of rectangle ABCD are
`4√(2) , 2√(2)`.

Diagonal of the rectangle ABCD =

`\sqrt{(4√(2))^2+(2√(2))^2} \\\\=√(32+8) \\\\=√(40)\\\\=2√(10) \\\\=6.3`

Hence, the length of a diagonal of a rectangle ABCD with vertices A (-3,1) B(-1,3) C (3,-1) is 6.3