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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.

Draw a line segment AB = 4.8 cm. Mark a point P outside the line segment AB. Construct a perpendicular to AB from P.

Learn how to construct a perpendicular from a point P to a line segment AB of 4.8 cm using a compass and ruler. This guide provides a step-by-step solution suitable for Grades 6-8.

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