Question

if the point (x,-1),(3,y),(-2,3)and (-3,-2) be the vertices of a parallelogram,then​ find the value of 2x+y​

Answer 1

Answer:The points A(x,−1),B(3,y),C(−2,3),D(−3,−2) are the vertices of a parallelogram..

We know that diagonals of a parallelogram bisect each other.

Let O be the point of bisection.

AO=OC and BO=OD

O is the midpoint of AC as well as BD.

Considering AC, O$(\frac{x-2}{2} ,\frac{-1+3}{2} )$

Considering BD, O$(\frac{3-3}{2} ,\frac{y-2}{2} )$

Equating the coordinates,

$\frac{x-2}{2} =0$

$x=2$

$\frac{y-2}{2} =2$

$y=4$