Answer:Answer:
the figure is parallelogram
Explanation:
enter image source here
As The mutually edges are parallel each other and equal,
the name of figure is parallelogram .
Step-by-step explanation:
Answer with explanation:
The vertices of Quadrilateral ABCD are ,A(−5,7), B(6,−3), C(10,2), and D(−1,12).
Distance formula between two points (a,b) and (c,d), is given by
[tex]=\sqrt{(a-c)^2+(b-d)^2[/tex]
[tex]AB=\sqrt{[-5-6]^2+[7-(-3)]^2}\\\\AB=\sqrt{121+100}\\\\AB=\sqrt{221}\\\\BC=\sqrt{[10-6]^2+(2+3)^2}\\\\BC=\sqrt{16+25}\\\\BC=\sqrt{41}\\\\CD=\sqrt{[10+1]^2+[2-12]^2}\\\\CD=\sqrt{121+100}\\\\CD=\sqrt{221}\\\\DA=\sqrt{[-1+5]^2+[12-7]^2}\\\\DA=\sqrt{16+25}\\\\DA=\sqrt{41}\\\\AC=\sqrt{[10+5]^2+[2-7]^2}\\\\AC=\sqrt{225+25}\\\\AC=\sqrt{250}\\\\BD=\sqrt{[6+1]^2+[-3-12]^2]}\\\\BD=\sqrt{49+225}\\\\BD=\sqrt{274}[/tex]
Opposite side of Quadrilateral[AB=CD, AD=BC] is equal, but Diagonals are not equal.
So, it is a Parallelogram.
