The task in the image asks you to draw a line segment $AB$ of length 4.8 cm, mark a point $P$ outside of this line, and then construct a perpendicular from point $P$ to the line segment $AB$.

Here is a step-by-step guide to solve this problem:

Step 1: Draw line segment $AB$

• Using a ruler, draw a straight line segment $AB$ of 4.8 cm.

Step 2: Mark point $P$

• Choose any point $P$ that is not on the line segment $AB$. This point should be outside the line.

Step 3: Construct a perpendicular from $P$ to $AB$

• With a compass, follow these steps:
  1. Place the compass at point $P$ and draw an arc that crosses the line segment $AB$ at two points. Let these points be $C$ and $D$.
  2. Without changing the compass width, place the compass on $C$ and draw an arc below or above the line.
  3. Do the same from point $D$, making sure that the two arcs intersect at some point. Let this point be $E$.
  4. Now, draw a straight line from $P$ through the point $E$. This line will be perpendicular to $AB$.

Step 4: Verify the perpendicularity

• The line from $P$ to $AB$ will form a right angle with the line segment $AB$.

Would you like further details on the geometric reasoning behind these steps?

Here are five related questions:

1. How can you confirm that two lines are perpendicular geometrically?
2. Can you construct a perpendicular without a compass, using only a protractor?
3. How does the perpendicular bisector differ from this perpendicular construction?
4. What are real-world applications of perpendicular line constructions?
5. How would you construct a parallel line instead of a perpendicular one?

Tip: Always keep your compass fixed when using it to ensure precision in constructions.