Chapter 12.8, Problem 23E

To determine

To find: The point that cannot be a vertex of rectangle.

Answer to Problem 23E

The point $\left(h,k\right)$ is not a vertex of a rectangle.

Explanation of Solution

Given information:

A rectangle with a length of $3h$ and a width of $k$ has a vertex at $\left(-h,k\right)$ .

  

Here,

it can be seen that it is a rectangle with the vertices $\left(-h,0\right),\left(2h,0\right),\left(2h,k\right),\left(-h,k\right)$ . The length of this graph is $3h$ its with is $k$ as given in the question.

From the above graph it can be seen that there is one point $\left(h,k\right)$ on this graph and it is not a vertex of the rectangle.

Therefore, the point $\left(h,k\right)$ is not a vertex of a rectangle.