JEE 1980's...

Geometry Level pending

If the two adjacent vertices of a parallelogram are A = ( − 2 , 4 ) A=(-2,4) and B = ( − 1 , 3 ) B=(-1,3) and the midpoint of the line joining the midpoint of opposite sides of the parallelogram lie on the positive x x -axis, find the coordinates of the other vertices if the area of the parallelogram is 12 .

If these coordinates can be expressed as ( x 1 , y 1 ) (x_1, y_ 1) and ( x 2 , y 2 ) (x_2, y_2) , then submit x 1 + x 2 + y 1 + y 2 x_1 + x_2 + y_1 + y_2 as your answer.


The answer is 28.

Vishwash Kumar Γξω by Vishwash Kumar ΓΞΩ , 19, India

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2 solutions

Ahmad Saad
Oct 10, 2016

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Just twisted , the midpoint of the line joining the midpoints of opp. sides of the || gm is the midpoint of its diagonal . i.e , it is the point of intersection of the diagonals of the || gm . Seems easy now . Just use the midpoint theorem on the diagonals .

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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