Question

What is wrong with each of the following instructions?

Draw the line through P and X parallel to $\overleftrightarrow{JE}$.

Short answer

The wrong statement in the given instruction is that the line through P and X is parallel to $\overleftrightarrow{JE}$. The line through P and X is not parallel to $\overleftrightarrow{JE}$ as the lines passing through P and X when extended intersects the line $\overleftrightarrow{JE}$.

Step-by-step solution

Step 1. Observe the given diagram.

The given diagram is:

Step 2. Draw the diagram depicting the given situation.

The diagram depicting the given situation is:

Consider a line joining the points P and X. When the line joining the points P and X is extended, it intersects the line $\overleftrightarrow{JE}$at the point N.

The parallel lines are the lines which are coplanar and do not intersect each other.

As, the line joining the points P and X and the line $\overleftrightarrow{JE}$are coplanar but they intersect each other, therefore the line joining the points P and X and the line $\overleftrightarrow{JE}$are not parallel.

Step 3. Description of step.

The wrong statement in the given instruction is that the line through P and X is parallel to $\overleftrightarrow{JE}$. The line through P and X is not parallel to$\overleftrightarrow{JE}$ as the lines passing through P and X when extended intersects the line $\overleftrightarrow{JE}$.