Chapter 1.5, Problem 6PSA

To determine

To Find : $\text{Whether M is the midpoint of }\overline{OP}\text{?}$

Explanation of Solution

Given information :

  $\begin{array}{l}OM=x+8\\ MP=2x-6\\ OP=44\end{array}$

  

Proof:

Here, we have

  $\begin{array}{l}OM=x+8\\ MP=2x-6\\ OP=44\\ \because OM+MP=OP=44\\ \Rightarrow x+8+2x-6=44\\ \Rightarrow 3x+2=44\\ \Rightarrow 3x=42\\ \Rightarrow x=14\\ \therefore OM=14+8=22\\ MP=2\times 14-6=22\end{array}$

Since, the measure of OM and MP are equal.

  $\text{Hence, M is the midpoint of }\overline{OP}\text{.}$