Question

If (x,3),(6,3),(8,2) and (9,4) are the vertices of a parallellogram taken in order ,then find the value of x and y.​

Answer 1

Answer:

Let A be the (x, 3), B be the (6,3), C be the (8,2) and D be the (9,4)

A = (x1,y1) = (x, 3)

B = (x2,y2) = (6,3)

C = (x3,y3) = (8,2)

D = (x4,y4) = (9,4)

It is given that ABCD is a parallelogram.

Diagonals of the parallelogram bisect each other.

Mid-point of AC = Mid-point of BD

Mid-point of AC = x1 + x3/2 , y1 + y3/2

= x + 8/2 , 3 + 2/2

= x + 8/2 , 5/2

Mid-point of BD = x2 + x4/2 , y2 + y4/2

= 6 + 9 /2 , 3 + 4/2

= 15/2 , 7/2

x + 8/2 = 15/2

x + 8 = 15

x = 15- 8

x = 7