Therefore it is a parallelogram.
Step-by-step explanation:
Given the vertices of the quadrilateral are A(2,3) , B(7,2), C(6,-1) and D(1,0)
The length of AB is [tex]=\sqrt{(2-7)^2+(3-2)^2}[/tex] [tex]=\sqrt{26}[/tex] units
The length of BC is [tex]=\sqrt{(7-6)^2+(2+1)^2}[/tex] [tex]=\sqrt{10}[/tex] units
The length of CD is [tex]=\sqrt{(6-1)^2+(-1-0)^2}[/tex] [tex]=\sqrt{26}[/tex] units
The length of DA is [tex]=\sqrt{(1-2)^2+(0-3)^2}[/tex] [tex]=\sqrt{10}[/tex] units
The length of AC is [tex]=\sqrt{(2-6)^2+(3+1)^2}[/tex] [tex]=4\sqrt{2}[/tex] units
The length of BD is [tex]=\sqrt{(7-1)^2+(2-0)^2}[/tex] = [tex]2\sqrt{10}[/tex] units
Here length of AB = length of CD ,
length of BC= length of DA and
length of AC ≠ length of BD
In this quadrilateral, the opposite sides are equal but the diagonals are not equal
Therefore it is a parallelogram.
