Question

Provide a counterexample to show that each statement is false.

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

Short answer

The counterexample is the diagram, which shows that the statement is false.

Step-by-step solution

Step 1. Define counterexample.

The counterexample is an example for which a hypothesis is true but the conclusion is false for an if-then statement.

Step 2. State counterexample.

For the given statement “If point G is on $\overrightarrow{AB}$, then G is on $\overrightarrow{BA}$.” let the counterexample by the figure given below:

Step 3. Verify the counterexample.

Here, point G is on $\overrightarrow{AB}$, because the line$\overrightarrow{AB}$ starts with A and then passes through point B and G, but the line $\overrightarrow{AB}$is starts from B and passes through A and does not pass through G.

Thus, the line $\overrightarrow{BA}$ does not pass-through point G.

Therefore, the diagram is a counterexample that shows that the statement is false.