Chapter 13.8, Problem 5WE

To determine

To find: The missing vertex of parallelogram given

Answer to Problem 5WE

The missing vertex is $\left(h+m,n\right)$ .

Explanation of Solution

Given information:Three vertices of the parallelogramare $(0,0)$ , $(h,0)$ and $(m,n)$ .

  

Calculation:

Let us give the name to the parallelogram as $\square OABC$ , where $O=(0,0)$ , $A\equiv (h,0)$ , $B\equiv (?,?)$ and $C\equiv (m,n)$

Since $\square OABC$ is parallelogram

  $\therefore OA=BC\text{ and }AB=OC$

The vertex $B$ can be labeled as $\left(h+m,n\right)$ .

Hence,

The missing vertex is $\left(h+m,n\right)$