Question

Three vertices of a kite ABCD are shown below. B(-3, 4) A(-5, 1) C(-1, 1)
What must the x-coordinate of vertex D be? Justify your answer ​

Answer 1

Answer:

Let the fourth vertex D =(x,y)

We know that the diagonals of a parallelogram bisect each other. So,the

midpoint of AC is same as the mid point of BD.

Mid point of two points (x1,y1) and (x2,y2) is  calculated by the formula (2x1+x2,2y1+y2)

So, midpoint of AC= Mid point of BD

=>(2−2+8,23+3)=(26+x,27+y)

=>(26,26)=(26+x,27+y)

=>6+x=6;7+y=6

=>x=0;y=−1

Hence, D=(0,−1)

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