Question

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

Answer 1

Step-by-step explanation:

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

AC and BD are the diagonals O is the mid-point of AC and BD .

if O is the mid-point of AC , then the coordinets 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

therefore, 1+x/2 = 7/2

=> 1+X =7

=> X= 7-1 = 6

therefore, 5+y/2 =4

=>5+y=8

=> y = 8-5

= 3

hence, X = 6 and Y=3