Chapter 2.1, Problem 13WE

To determine

To prove:that the statement is false and give a counter example

Explanation of Solution

Given information:

The given statement is:

If point $G$ is on $\overrightarrow{AB},$ then $G$ is on $\overrightarrow{BA}$

Consider the diagram

Here $G$ is on $\overrightarrow{AB}$ because $\overrightarrow{AB}$ starts from $A$ and going through $B$ and $G$

But $\overrightarrow{BA}$ is start from $B$ and going only through $A$

Thus, $G$ is not on $\overline{BA}$

Hence, our statement is false.

A counter example is such an example which shows the given statement is false

Therefore, the above diagram is a counter example.