Question

The rhombus has vertices K(w, 0), M(w, v), and L(u, z). Which of the following could be coordinates of N?

(u, 0)


(v, w)


(0, z)


(z, 0)

Answer 1

Answer with explanation:

Vertices of Rhombus, KM LN, are : K (w,0), M (w,v) , L (u,z) and N (?).

N (?)= (x,y)

Diagonals of Rhombus Bisect each other.Diagonal, KL and MN will Bisect each other.

Mid Point Formula of Line Joining , (m,n ) and (r,s) is :

`=((m+r)/(2),(n+s)/(2))`

Mid Point of KL is

`=((w+u)/(2),(0+z)/(2))`

Mid Point of MN is

`=((w+x)/(2),(v+y)/(2))`

So, Mid point of KL = Mid Point of MN

`((w+u)/(2),(0+z)/(2))=((w+x)/(2),(v+y)/(2))\\\\ (w+u)/(2)=(w+x)/(2)\\\\x=u\\\\(0+z)/(2)=(v+y)/(2)\\\\y=z-v`

So, coordinates of Point N,can be = (u, z-v).

None, of the Option,matches with the given option.

If you will Write the rhombus as,K L MN,then also you will not get answer which matches with the options.

Answer 2

the answer would be the third choice which is N(0, z)