Determine whether the quadrilateral is a parallelogram using the specified method. D(-8, 1), E(-3, 6), F(7, 4), G(2, -1)

To determine whether the quadrilateral is a parallelogram or not first we have to the properties of parallelogram. One of them is Opposite sides of parallelogram are congruent or equal.

Given that:- D(-8,1), E(-3,6), F(7,4), G(2,-1) are sides of a quadrilateral

if opposite sides of this quadrilateral is equal then it is proof that this quadrilateral is a parallelogram

by using distance formula=root (x2-x1)^2+(y2-y1)^2

first, distance of DE=root (-3+8)^2+(6-1)^2

                                    =root (5)^2+(5)^2

                                     =root 25+25

                                     =root 50

                                     =5 root 2

next, distance of EF=root (7+3)^2+(4-6)^2

                                    =root (10)^2+(-2)^2

                                     =root 100+4

                                     =root 104

next, distance of FG=root (2-7)^2+(-1-4)^2

                                    =root (-5)^2+(-5)^2

                                     =root 25+25

                                     =root 50

                                     =5 root 2

next, distance of DG=root (2+8)^2+(-1-1)^2

                                    =root (10)^2+(-2)^2

                                     =root 100+4

                                     =root 104

here, DE=FG and EF=DG, hence this quadrilateral is a parallelogram beacuse its opposie sides are equal.