Question

If (3,3),(6,y),(x,7) and (5,6)are the vertices of a parallogram taken in order, find the values of x and y

Answer 1

Let A(3, 3), B(6, y), C(x, 7) and D(5, 6) be the vertices of a ll gm ABCD. Join AC and BD, intersecting each other at the point O.
We know that the diagonals of llgm bisect each other.
Therefore, O is the midpoint of AC as well as that of BD.
`therefore "midpoint of AC is "((x+3)/(2), (7+3)/(2)), i.e., ((x+3)/(2), 5) "and midpoint of BD is"((5+6)/(2), (6+4)/(2))i.e., ((11)/(2), (6+y)/(2)).`
But, these points coincide at the point O.
`therefore (x+3)/(2) = (11)/(2) "and" (6+y)/(2) = 5`
`rArr x + 3 = 11 "and" 6+y = 10`
`rArr` x= 8 and y =4.
Hence, x = 8 and y = 4.