Question

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

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 :

            $=(\frac{m+r}{2},\frac{n+s}{2})$

Mid Point of KL is

         $=(\frac{w+u}{2},\frac{0+z}{2})$

Mid Point of MN is

         $=(\frac{w+x}{2},\frac{v+y}{2})$

So, Mid point of KL = Mid Point of MN

$(\frac{w+u}{2},\frac{0+z}{2})=(\frac{w+x}{2},\frac{v+y}{2})\\\\ \frac{w+u}{2}=\frac{w+x}{2}\\\\x=u\\\\\frac{0+z}{2}=\frac{v+y}{2}\\\\y=z-v$

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)