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

The answer is (d,c)!!!

Answer 2

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

`=((p+r)/(2),(q+s)/(2))`

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

`=((a+a)/(2),(0+b)/(2))\\\\=((2a)/(2),(b)/(2))\\\\=(a,(b)/(2))`

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

`=((x+0)/(2),(y+c)/(2))\\\\=((x)/(2),(y+c)/(2))`

As, Diagonal bisect each other,so

`a=(x)/(2)\\\\x=2 a\\\\ (y+c)/(2))=(b)/(2)\\\\y=b-c`

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