Question

The coordinates of the vertices of quadrilateral ABCD are A(0,4), B(4,2), C(2,-1), and D(-2,1). Jorge states that quadrilateral ABCD is a parallelogram. Prove or disprove Jorge’s statement? Help solve answer

Answer 1

Slope of AB `=m_(AB)=(4-2)/(0-4)=-1/2`

Slope of BC `=m_(BC)=(2-(-1))/(4-2)=3/2`

Slope of CD `=m_(CD)=(-1-1)/(2-(-2))=-1/2`

Slope of DA `=m_(DA)=(1-4)/(-2-0)=3/2`

Since

`m_(AB)=m_(CD)=1/2->AB"||"CD`

`m_(BC)=m_(DA)=-3/2->BC"||"DA`

Hence quadrilateral `ABCD` is a parallelogram