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If (-6,-4) and (3,5) are the extremities of the diagonals of a parallelogram and (2,-1) is its third vertex, then its fourth vertex is

If (-6,-4) and (3,5) are the extremities of the diagonals of a parallelogram and (2,-1) is its third vertex, then its fourth vertex is

Grade:11

1 Answers

Raghav Rao
40 Points
6 years ago
Let P(-6,-4) Q(2,-1) R(3,5) S(x,y)
The two diagonals of a parallelogram bisect each other. So the midpoint of PR = midpoint of QS 
so using that midpoint of PR = (-6+3)/2 , (-4+5)/2  )   =(-3/2,1/2)
=>midpoint of QS= (-3/2,1/2) ={(2+x)/2 ,(-1+y)/2}
=>s=(-5,2).
 

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