Chapter 1.3, Problem 31WE

(a)

To determine

To find: the distance of the $\overline{RS}$ .

Answer to Problem 31WE

The distance of the $\overline{RS}$ is $5$ .

Explanation of Solution

Given:

The distance are $QR=4$ and $ST=5$ .

Calculation:

As the point S is the midpoint of $\overline{RT}$ .

So, the distance between $\overline{RT}$ and $\overline{RS}$ must be same.

So, the distance $\overline{RS}=5$ .

Therefore, the distance of the $\overline{RS}$ is $5$ .

(b)

To determine

To find: the distance of the $\overline{RT}$ .

Answer to Problem 31WE

The distance of the $\overline{RT}$ is $10$ .

Explanation of Solution

Given:

The distance are $QR=4$ and $ST=5$ .

Calculation:

As the point S is the midpoint of $\overline{RT}$ .

So, the distance between $\overline{RT}$ and $\overline{RS}$ must be same.

Find the distance $\overline{RT}$ .

  $\begin{array}{c}\overline{RT}=\overline{RS}+\overline{ST}\\ =5+5\\ =10\end{array}$

Therefore, the distance of the $\overline{RT}$ is $10$ .

(c)

To determine

To find: the distance of the $\overline{PR}$ .

Answer to Problem 31WE

The distance $\overline{PR}$ is $10$ .

Explanation of Solution

Given:

The distance are $QR=4$ and $ST=5$ .

Calculation:

As the line $\overline{PR}\cong \overline{RT}$ .

So, the distance between $\overline{PR}$ and $\overline{RT}$ must be same.

Then, the distance $\overline{PR}$ is $10$ .

Therefore, the distance $\overline{PR}$ is $10$ .

(d)

To determine

To find: the distance of the $\overline{PQ}$ .

Answer to Problem 31WE

The distance $\overline{PQ}$ is $6$ .

Explanation of Solution

Given:

The distance are $QR=4$ and $ST=5$ .

Calculation:

As the line $\overline{PR}\cong \overline{RT}$ .

So, the distance between $\overline{PR}$ and $\overline{RT}$ must be same.

Find the distance $\overline{PQ}$ .

  $\begin{array}{c}\overline{PQ}=\overline{PR}-\overline{QR}\\ =10-4\\ =6\end{array}$

Therefore, the distance $\overline{PQ}$ is $6$ .