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)
