Chapter 5.4, Problem 39WE

To determine

ToPlot: the points of the vertices of a rhombus whose three vertices are $O\left(0,0\right),S\left(0,10\right),E\left(6,18\right)$ ,finds fourth vertex and measure side to check the answer.

Answer to Problem 39WE

  $W\left(6,8\right)$

Explanation of Solution

Given:

Three vertices are $O\left(0,0\right),S\left(0,10\right),E\left(6,18\right)$ .

Calculation:

Since, all sides of a rhombus are equal therefore fourth coordinate is $W\left(6,8\right)$ .

Points are plotted as shown below.

  

Length of side OS.

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

Length of SE is.

  $\begin{array}{l}SE=\sqrt{{\left(18-10\right)}^2+{\left(6-0\right)}^2}\\ SE=\sqrt{64+36}\\ SE=10\end{array}$

Length of EW.

  $\begin{array}{l}EW=\sqrt{{\left(18-8\right)}^2+{\left(6-6\right)}^2}\\ EW=\sqrt{100+0}\\ EW=10\end{array}$

Length of WO.

  $\begin{array}{l}WO=\sqrt{{\left(8-0\right)}^2+{\left(6-0\right)}^2}\\ WO=\sqrt{64+36}\\ WO=10\end{array}$

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

Therefore, the answer is $W\left(6,8\right)$