Question

Calculate the coordinates of d so that the quadrilateral abcd formed by the vertuces a=(-1,-2), b=(4,-1),c=(5,2) and d=(?,?) is a paralellogram

Answer 1

As diagonals of a parallelogram bisect each other.

Then O is the mid point of lines AC and BD

Mid point = (x₁+x₂)/2  ,  (y₁+y₂)/2

Then In line AC → O(a,b) = (-1+5)/2 , (-2+2)/2

                                          = 4/2  ,  0/2

                               O(a,b) = (2,0)
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In line BD → O(2,0) = (4+x)/2  ,  (-1+y)/2

Taking x coordinate

2 = 4+x/2

x = 4 - 4  ⇒  x = 0

Then taking y coordinate

0 = -1+y/2

0 = y - 1 ⇒ y = 1
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So D(x,y) = D(0,1)
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☺☺☺ Hope this Helps ☺☺☺

Answer 2

Answer:

Step-by-step e