91Ó°ÊÓ

Coordinates of the three vertices are $\text{O}\left(0,0\right)\text{,S}\left(0,10\right)\text{,E}\left(6,18\right)$.

Since it is a rhombus, therefore, it’s all four sides will be equal.

Give coordinates are plotted below:

For the fourth coordinate.

Since in rhombus all sides are equal, therefore, point W will be 6 units to the right of O as E is 6 units to the right of S.

X - coordinate of W is:

$\begin{array}{c}X=0+6\\ =6\end{array}$

Since the point O is 10 units below S, point W must be 10 units below E. So, Y coordinate of W is will be:

Y - coordinate of W is:

$\begin{array}{c}Y=18−10\\ =8\end{array}$

So, coordinates of W will be $\left(6,8\right)$.

Length of side OS :

$\begin{array}{c}OS=\sqrt{{\left(10−0\right)}^2+{\left(0−0\right)}^2}\\ =\sqrt{100}\\ =10\end{array}$

Length of side SE:

$\begin{array}{c}SE=\sqrt{{\left(18−10\right)}^2+{\left(6−0\right)}^2}\\ =\sqrt{100}\\ =10\end{array}$

Length of side EW:

$\begin{array}{c}EW=\sqrt{{\left(18−8\right)}^2+{\left(6−6\right)}^2}\\ =\sqrt{100}\\ =10\end{array}$

Length of side WO:

$\begin{array}{c}WO=\sqrt{{\left(8−0\right)}^2+{\left(6−0\right)}^2}\\ =\sqrt{100}\\ =10\end{array}$

Since all sides are equal, therefore, it is a rhombus and the fourth vertex is $\left(6,8\right)$.

Therefore, the fourth vertex is $W\left(6,8\right)$.