(Q26) If (1,2),(4,y),(x,6) and (3,5) are the vertices of a parallelogram taken in order, find x and y.

Answer

ABCD

Given ABCD is a parallelogram

where A(1,2),B(4,y),C(x,6) and D(3,5).

In a parallelogram, diagonals bisect each other.

The midpoint of the diagonals coincide with each other.

Midpoint of AC=midpoint of BD

Midpoint = (
x1+x2
2
 ,
y1+y2
2
)
= (
+x
2
 ,
+
2
) = (
+
2
 ,
y+
2
)
=
+x
2
 =
2
 and
2
 =
y+
2

+x= and =y+

x=- and y=-

x= and y=.