Question

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

Answer 1

3

Step-by-step explanation:

let A( 1,2) B (4,y ) C( x ,6) and D (3 ,5) are the vertices of a parallelogram ABCD

.AC and BD are the diagonals .

O is the midpoint of AC and BD .

if O is the mid point of AC, then the

coordinates of O are = (1+ x/2, 2+6 /2)=( x+1/2,4)

if O is the midpoint of BD then coordinates of O (4+3/2,5+y/2) =( 7/2 , 5+y /2 )

since both coordinates are of the same point O

: 1+x /2 =7/2

implies that 1+x = 7

implies that x = 7 -1 =6

: 5+y by 2 = 4

implies that 5+ y =8

implies that y = 8 -5 =3

Hence x=6 and y = 3