Answer:
[tex]|SU|=\sqrt{13}[/tex]
Step-by-step explanation:
The given parallelogram has vertices R(1, -1), S(6, 1), T(8, 5), and U(3, 3) .
Recall the distance formula;
We use the distance formula to determine the length of the diagonals.
For diagonal R(1,-1) and T(8,5), We have;
[tex]|RT|=\sqrt{(8-1)^2+(5--1)^2}[/tex]
[tex]|RT|=\sqrt{(7)^2+(6)^2}[/tex]
[tex]|RT|=\sqrt{49+36}[/tex]
[tex]|RT|=\sqrt{85}[/tex]
For the diagonal S(6,1) U(3,3)
[tex]|SU|=\sqrt{(6-3)^2+(5-3)^2}[/tex]
[tex]|SU|=\sqrt{(3)^2+(2)^2}[/tex]
[tex]|SU|=\sqrt{9+4}[/tex]
[tex]|SU|=\sqrt{13}[/tex]
Therefore the shorter diagonal is:
[tex]|SU|=\sqrt{13}[/tex]
