Question

if the three vertices of a parallelogram are (a+b,a-b), (2a+b,2a-b) and (a-b,a+b), then the fourth vertex is ???

Answer 1

find the midpoints of diagonals and equate it to 2a/2 to the coordinates.


hope it helps........!!

Answer 2

Answer:

$\red { Fourth \: vertex=(x_{4},y_{4})} =\green { (-b,b)}$

Step-by-step explanation:

Given (a+b,a-b) , (2a+b,2a-b) and (a-b,a+b) are three verticies of a parallelogram.

$Let \: A (a+b,a-b) = (x_{1},y_{1}) ,<strong> </strong>\\ B(2a+b,2a-b) = (x_{2},y_{2}) , \\ C(a-b,a+b) = (x_{3},y_{3}) , \\and \: D(x_{4},y_{4})$

$\blue {x_{4} }= x_{1}+x_{3}-x_{2}$

$= a+b+a-b-(2a+b)\\=2a-2a-b\\=\blue {-b}$

$\orange {y_{4}} =y_{1}+y_{3}-y_{2}$

$= a-b+a+b-(2a-b)\\=2a-2a+b\\=\orange {b}$

Therefore.,

$\red { Fourth \: vertex=(x_{4},y_{4})} =\green { (-b,b)}$

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