Question

Prove thst A(-2,-1),B(1,0)C(4,3) D(1,2)are the vertices of a parallelogram

Answer 1

u find the slope of all lines ...and then u will observe that slope of two lines will be equal to each other....and hence the same with other two lines..!!!
and like this way u can prove that the given points are the vertices of parallelogram

Answer 2

let ABCD is a parallelogram where AB||CD and AD||BC
Since in a parallelogram side AB=sideCD
and side AD=side BC
so AB=root [(-2-1)^2+(-1-0)^2]=root 10
and CD=root [(4-1)^2+(3-2)^2]=root 10
so here AB=CD
Again AD=root[(-2-1)^2+(-1-2)^2]=root 18
and BC=root [(1-4)^2+(0-3)^2)]=root 18
so AD=BC
hence ABCD is a parallelogram with the given vertices