## Drawing a Perpendicular from the End Point of a Line

**How to draw a perpendicular line from the end point of the line**

**What You Start With**

Shown above is a line of any length and a point P on the end of the line. The point P can also be on the other side of the line. The line can also be at any angle for this principle to work.

**The Theory Behind How It Works**

To start off we pick a random point 'A'

**Proof:**- The reason that this method works is because by taking the distance PA as the radius means that the distance from CB is the diameter of the circle.
- We already know that if a triangle has one side as the diameter and the third vertex anywhere on the circumference of the circle, then the triangle will always be a right-angled triangle.
- Therefore line PC is perpendicular to line PB as required.

**Alternate Method:**

An alternative way of completing the questioning is by extending the given line and use the method previously explained in the section 'Perpendicular to a line on a point'

Click the link below to see this explained in more detail.