Chapter 5.4, Problem 38WE

To determine

To Find: the coordinates of fourth vertex V of the rhombus such that other coordinates of three vertices are $O\left(0,0\right),L\left(5,0\right),D\left(4,3\right)$ .

Answer to Problem 38WE

  $(9,3)$

Explanation of Solution

Given Coordinates of thee vertices are $O\left(0,0\right),L\left(5,0\right),D\left(4,3\right)$ .

Calculation:

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

Given coordinated are plotted below.

  

For the fourth coordinate.

Since, in rhombus all sides are equal therefore point V will be 5 units to the right of D as L is 5 units to the right of O .

X -coordinate of V is.

  $\begin{array}{l}=4+5\\ =9\end{array}$

Y -coordinate of V is.

Since, point D is 3 units in y direction from O so y coordinate of V will be 3 units.

So, coordinates of V will be $(9,3)$ as plotted below.

  

Measure of side AB.

  $\begin{array}{l}=5-0\\ =5\end{array}$

Measure of side CD.

  $\begin{array}{l}=9-4\\ =5\end{array}$

Measure of side AD.

  $\begin{array}{l}=\sqrt{{\left(3\right)}^2+{\left(4\right)}^2}\\ =\sqrt{25}\\ =5\end{array}$

Measure of side BC.

  $\begin{array}{l}=\sqrt{{\left(9-5\right)}^2+{\left(3\right)}^2}\\ =\sqrt{25}\\ =5\end{array}$

Since, all sides are equal to 5 unit therefore it is a rhombus and fourth vertex is $(9,3)$ .