Given vertices ofQuadrilateral RSTU as R(1,3), S(4,1), T(1,-3) and U(-2,-1).
We need to check if diagonals are congruent.
The coordinates of verticales diagonal RT are R(1,3) and T(1,-3).
The coordinates of verticales diagonal SU are S(4,1), and U(-2,-1),
By applying distance formula:
[tex]\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
RT = [tex]=\sqrt{\left(1-1\right)^2+\left(-3-3\right)^2}[/tex]=[tex]\sqrt{36}[/tex]
RT = 6
SU [tex]=\sqrt{\left(-2-4\right)^2+\left(-1-1\right)^2}[/tex].
[tex]=2\sqrt{10}[/tex].
Diagonal RT is not congruent to Diagonal SU.
Therefore, Quadrilateral RSTU is not a rectangle because the diagonals are not congruent.
So, it is False.
