Question

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

find x and y.​

Answer 1

Step-by-step explanation:

here is your ans frnd

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 mid-point of BD then coordinates of O are ( 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

⇒1+x=7

⇒x=7−1=6

∴ 5+y/2=4

⇒5+y=8

⇒y=8−5

therefore x=6 and y=3.