Answer:
[tex]AC = BD = 5.7[/tex]
Step-by-step explanation:
Given
[tex]A = (1,3)[/tex]
[tex]B = (5,3)[/tex]
Required
The length of the diagonals
First, calculate the length of AB using:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
So, we have:
[tex]AB = \sqrt{(1 - 5)^2 + (3 - 3)^2}[/tex]
[tex]AB = \sqrt{(-4)^2 + 0^2}[/tex]
[tex]AB = \sqrt{16}[/tex]
[tex]AB = 4[/tex]
The diagonal of a square is calculated using:
[tex]Diagonal = x\sqrt{2[/tex]
Where x is the length of each side.
So:
[tex]AC = BD = AB\sqrt{2}[/tex]
[tex]AC = BD = 4\sqrt{2}[/tex]
[tex]AC = BD = 5.7[/tex] -- approximated
