CBSE Class 10 Answered

we know that the diagonals of a parallelogram bisect each other.

 it means that the point of  their intersection is the mid point of each diagonal.

let the point of int. be P(q,r)

so

A,B ,C are the given three points (in the same order as in the question)

then mid point of AC is P

and

 mid point of BD is P.

so, using mid point formula  for AC, we get,

{[(a+b)+(a-b)]/2}  ,{[(a-b)+(a+b)]/2}=(q,r)

solving we get,

p=a, q=a

 now using the midpoint formula for BD we get

[x+(2a+b)]/2  ,[y+(2a-b)]/2=(a,a)

solving we get

x= -b, y=b