Question

The fourth vertex D of a parallelogram ABCD whose three vertices are A(-2,3) , B(6,7) , C(10,3) is __________.​

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 ( x1+x2/2) , (y1+y2)

So, midpoint of AC= Mid point of BD

=>( −2+10/2 , 3+3/2 ) = ( 6+x/2 , 7+y/2 )

=>( 4/2 ,6/2) = ( 6+x/2 , 7+y/2 )

=> 6+x = 4 , 7+y = 6

=> x = -2 , y = -1

=>x= -2 ; y = -1

Hence, D=(-2,−1)

hope it helps you