Question

How many lines can be drawn through P perpendicular to $\overleftrightarrow{QR}$?

Short answer

The required count of line is one.

Step-by-step solution

Step 1. Define the theorem that can be used

Theorem 3-8 can be used which states that a perpendicular line to another line consist of a point that is positioned on outer area of another line.

Step 2. Relate the theorem using the provided information

The mentioned point in theorem according to the question is P and the another line is $\overleftrightarrow{QR}$. According to the figure there is only one line present that is having a perpendicular relation with $\overleftrightarrow{QR}$and contains point P.

Step 3. Make the conclusion

As the count of line perpendicular to $\overleftrightarrow{QR}$is only one which results in that the required count is one.