Select the correct answer.

What is the first step in the construction of a line perpendicular to A⁢B⟷ and passing through an external point *M*? Assume that the construction uses only a compass and a straightedge.

 **A.** 

Place the compass needle on *M* and, keeping the compass width the same, draw two arcs that intersect A⁢B⟷.

 **B.** 

Place the compass needle at any point on A⁢B⟷, and set the compass width to *M*.

 **C.** 

Draw a line from point *M* passing through A⁢B⟷, and mark the point of intersection.

 **D.** 

Place the compass needle at any two points on A⁢B⟷, and draw two arcs through *M*.


The correct answer is **A**.

**Explanation**: The first step in constructing a line perpendicular to line \( AB \) and passing through an external point \( M \) using a compass and straightedge is to place the compass needle on \( M \), then draw two arcs that intersect the line \( AB \). These intersections help in the next steps of the construction to create the perpendicular line.

Would you like a detailed explanation of the construction process?

### Related Questions:
1. What is the next step after drawing the two arcs that intersect \( AB \)?
2. How do you confirm that the line drawn is truly perpendicular to \( AB \)?
3. Why is it important to keep the compass width the same while drawing the arcs?
4. Can this construction method be used to create a perpendicular bisector?
5. How would you construct a parallel line through \( M \) instead of a perpendicular line?

**Tip:** Always ensure the compass width remains constant during the construction for accurate results.

Learn how to construct a perpendicular line to line AB passing through external point M using compass and straightedge. Step-by-step explanation with detailed instructions. Suitable for high school geometry students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation