Question

If (1,2), (4,y), (x,6), and (3,5) are the vertices of a parallelogram taken in order find x,y . ONLY BEST ANS NEED in pic OR WILL BE REPORTED

Answer 1

Let the A=(1,2),B=(4,y),C=(x,y),D=(3,5)
(1+x2,(2+6)2)=((1+x)2,4)
((4+3)2,(5+y)2)=(72,(5+y)2)
According to condition(1)=1+x)2=72
=(1+x)=7
=x=6
According to condition(2)=4=5+y2
=8=5+y
=y=3
So, therefore x=6 and y=3

Answer 2

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Hey mate !!

Here's your answer !!

Since it is a parallelogram , the diagonals bisect each other. 

So the diagonals are equal at the centre point O.

=> O acts as the mid point for the lines AC and BD.

Hence lets take the line AC:

Coordinates of O are x` and y`

Where x` = ( x₁ + x₂ / 2) 

y` = ( y₁ + y₂ / 2 )

So x` = ( 1 + x / 2 )  and

y` = (2 + 6 / 2 ) = ( 8 / 2 ) = 4.

=> y` = 4

So Coordinates of O =  (1 + x / 2 , 4 )   -----(1)

Since it is the midpoint of BD also the same formula gets repeated here.

So x¹ = ( 4 + 3 / 2 ) = 7 / 2

y¹ = ( 5 + y / 2 )

So Coordinates of O = ( 7 / 2 , 5 + y / 2) -----(2)

Since O cannot be different the values are same. So lets find x and y by substituting the value with each other that we got in (1) and (2)

X` = X¹ , Y` = Y¹

So first lets solve X,

= 1 + X / 2 = 7 / 2

= 1 + X = 7     ( Since 2 gets cancelled on both sides )

= x = 7 - 1 = 6

So X = 6

Now lets solve Y

= 4 = 5 + y / 2

Transposing 2 that side we get,

= 4 × 2 = 5 + y

= 8 = 5 + y

= 8 - 5 = y

=> 3 = y 

Hence values of  X and Y are 6 and 3 respectively.

Hope this helps !!

Cheers !!
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# Kalpesh :)