IIT JEE , AIEEE Forum - Mathematics , Analytical Geometry - IF THE GIVEN THREE POINTS ARE CONSECUTIVE VERTICES OF A PARALLELOGRAM THEN FOURTH VERTEX

sankydreams

Simple ques
Look since the diagnols of parallelogram bisect each other, their mid points will be same
Now we have been given with three consecutive vertices
(x1,y1) and (x3,y3) will be opposite vertices
x coordinate of mid point of these vertices = (x1 + x3) / 2
Let the fourth vertex be (x,y)
So x coordinat of mid point of (x2,y2) and (x,y) = (x+x2) / 2
Since the mid points coincide,
(x1 + x3)/ 2 = (x+x2) /2
=> x = x1-x2+x3
y coordinate in the same way will be y1 - y2 + y3
So ans is (b)
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