How to draw a perpendicular line through a point.

Introduction

This tutorial guides you through the process of drawing a perpendicular line through a given point onto an existing line. Understanding how to accurately create perpendicular lines is essential in geometry and can be applied in various fields, including engineering, architecture, and design.

Step 1: Gather Your Materials

Before you start drawing, ensure you have the following materials:

• A straightedge or ruler
• A compass
• A pencil
• Paper

Step 2: Draw the Base Line

Start by drawing a straight line on your paper:

1. Use your straightedge or ruler to create a horizontal line.
2. Label this line as Line A for reference.

Step 3: Mark the Given Point

Select and mark the point through which you want to draw the perpendicular line:

1. Choose a point on or above Line A.
2. Clearly label this point as Point P.

Step 4: Set the Compass Width

Next, adjust your compass to a suitable width for drawing arcs:

1. Place the compass point on Point P.
2. Draw an arc that intersects Line A at two points. Label these intersection points as A1 and A2.

Step 5: Draw the Arcs

Using the compass:

1. Without changing the width, place the compass point on Point A1.
2. Draw an arc above and below Line A.
3. Repeat this step with the compass point on A2, creating two more arcs that intersect the previous arcs.

Step 6: Connect the Intersections

Identify the points where the arcs intersect and draw the perpendicular line:

1. Label the intersection points of the arcs as I1 and I2.
2. Use your straightedge to draw a line through Point P and the intersection points I1 and I2.

Step 7: Finalize the Perpendicular Line

Ensure the line is clearly marked:

1. Highlight the perpendicular line you have drawn.
2. Confirm that the angle formed between the new line and Line A is 90 degrees, indicating a proper perpendicular.

Conclusion

You have successfully drawn a perpendicular line through a given point onto an existing line. This method can be applied in various geometric constructions and is foundational for more complex designs. Practice this technique to enhance your skills in geometry, and consider exploring other geometric constructions as your next step.