Question

The rhombus has vertices K(a, 0), M(a, b), and N(0, c). Which of the following could be coordinates of L?

Answer 1

Answer with explanation:

The Vertices of Rhombus K L MN are ,  K(a, 0), M(a, b), and N(0, c).

Let Coordinates of Vertices of Point L ,which is one of the vertices among four vertices = (x,y)

As, Diagonals of rhombus bisect each other.

We will use the mid point formula ,to find the vertex of point L.

Mid Point Formula, of line joining two points , (p,q) and (r,s) is

       $=(\frac{p+r}{2},\frac{q+s}{2})$

Mid Point of ,K(a,0) and M (a,b) is

      $=(\frac{a+a}{2},\frac{0+b}{2})\\\\=(\frac{2a}{2},\frac{b}{2})\\\\=(a,\frac{b}{2})$

Mid Point of L (x,y) and N (0,c) is

    $=(\frac{x+0}{2},\frac{y+c}{2})\\\\=(\frac{x}{2},\frac{y+c}{2})$

As, Diagonal bisect each other,so

  $a=\frac{x}{2}\\\\x=2 a\\\\ \frac{y+c}{2})=\frac{b}{2}\\\\y=b-c$

Coordinates of vertices of L are =(2 a, b-c)

Answer 2

The answer is (d,c)!!!