Question

If the points A(1,-2) B(2,3) C(x,2) D(-4,-3) form a parallelogram. Find x and also the height of the parallelogram by taking AB as the base

Answer 1

Heya !!!


A(1,-2) , B(2,3) , C(X,2) and D(-4,-3) be the vertices of a parallelogram ABCD . Join AC and BD , Intersecting each other at the point Of.

We know that the diagonals of parallelogram bisect eaach other.


Therefore,


O is the midpoint of AC as well as BD.



Therefore,

A (1,-2) and C (X,2)


Here,


X1 = 1 , Y1 = -2 and X2 = X , Y2 = 2



Midpoint of AC is ( X1+X2/2 , Y1+Y2/2) => ( 1+X/2 , -2 + 2/2 ) => ( 1+X/2 , 0/2)


And,



B(2,3) and D(-4,-3)


Here,


X1 = 2 , Y1 = -4 and X2 = -4 , Y2 = -3



Midpoint of BD is ( X1+X2/2 , Y1+Y2/2) => ( 2+(-4)/2 , ( -4 + (-3) /2 )


=> ( 2 -4/2 , -4 -3 /2)


=> ( -2/2 , -7/2) = ( -1 , -7/2)



Therefore,


( 1+X/2) = -1



1+ X = -2


X = -2 -1


X = -3



HOPE IT WILL HELP YOU..... :-)