A(a,b), B(a3,b4),C(a-1,b7) are the vertices of parallelogram ABCD find the coordinate of D Earlier answer provuded to me - Maths -

Question

A(a,b), B(a3,b4),C(a-1,b7) are the vertices of parallelogram ABCD
find the coordinate of D Earlier answer provuded to me did not
clear my doubts since there are two different variables a, b here
leaving apart the coordinates of D Pls solve for a and b

Mayank Jha · Accepted Answer

Dear student,

I am assuming the vertices as
A(a, b), B(a3,b3) and C(a - 1, b7)
Let the co-ordinates of point D be (x , y)

Then,

Mid point of AC = (a + a - 12, b + b72) = (a, b + b72)Mid point of BD = (a3+ x2, b3 + y2)Since diagnals of a parallelogram bisect each other
∴Mid point of AC = Mid point of BD(a, b + b72) = (a3+ x2, b3 + y2)⇒a3+ x2 = a and  b + b72 = b3 + y2⇒x = 2a - a3 and y = b + b7 - b3

Regards

A(a,b), B(a3,b4),C(a-1,b7) are the vertices of parallelogram ABCD. find the coordinate of D. Earlier answer provuded to me did not clear my doubts since there are two different variables a, b here leaving apart the coordinates of D. Pls solve for a and b.