Chapter 15.1, Problem 6PSA

a.

To determine

To explain: that how $PX$ is related to $PQ$ of the given equation.

Answer to Problem 6PSA

  $PX<PQ$ .

Explanation of Solution

Given:

The given condition: $X$ is between $P$ and $Q$

Calculation:

According to the question, $X$ is between $P$ and $Q$ , then

  $PX+XQ=PQ$

Therefore, it is simply said that $PX<PQ$ .

b.

To determine

To explain: that how $PX$ is related to $PQ$ of the given equation as an inequality.

Answer to Problem 6PSA

  $PX<PQ$ .

Explanation of Solution

Given:

The given condition: $X$ is the mid-point $P$ and $Q$

Calculation:

According to the question, $X$ is the mid-point $P$ and $Q$ , then

  $PX+XQ=PQ$

Therefore, it is simply said that $PX<PQ$ .

c.

To determine

To explain: that how $PX$ is related to $PQ$ of the given equation as an equality.

Answer to Problem 6PSA

  $PQ=2PX$ .

Explanation of Solution

Given:

The given condition: $X$ is the mid-point $P$ and $Q$

Calculation:

According to the question, $X$ is the mid-point $P$ and $Q$ , then

  $\begin{array}{l}PX=QX\\ \Rightarrow PX+XQ=PQ\\ \Rightarrow 2PX=PQ\end{array}$

Therefore, it is clearly seen that $PQ=2PX$ .