In these lessons, we will learn

- how to construct a perpendicular to a line, through a point on a line.
- how to construct a perpendicular to a line, through a point not on a line.

We will now show how to construct a perpendicular to a line segment, through a point on the line.

*Example : *

Construct a line perpendicular to *PQ* through the point *R* on *PQ*.

* Solution: *

**Step 1: **Stretch your compasses a short length. It can be any length. Put the sharp end of the compasses on point *R* and mark two arcs *S* and *T* on the line *PQ.*

** Step 2:** Stretch the compasses a little more. Put the sharp end of the compasses on point *S* and make an arc with pencil end. Do the same on point *T* but make sure that the second arc intersects the first arc.

**Step3:** Draw a line from point *R* to the point where the arcs intersect. This line is perpendicular to *PQ* and passes through the point *R.*

1. Place compass point on the given point, and draw arc either side of point such that it intersects line twice.

2. Place compass on each arc-line intersection, and draw an arc above the line, without changing the compasses' width.

3. Using a straight edge, connect this intersection point to the original point with a straight line.

We will now construct a perpendicular to a line, through a point not on the line.

* Example* :

Construct a line perpendicular to the line *AB* and passing through the point *P, *that is not on the line,

* Solution: *

** Step 1:** Put the sharp end of your compasses on point *P,* stretch the compasses and mark two arcs *R* and *S* on the line *AB. *

Step2: Without changing the width of the compasses, put the sharp end of the compasses at *R* and draw an arc on the other side of *AB* compared with *P*. Do the same at *S* and make sure that the second arc intersects the first arc.

**Step 3 : **Draw a line from *P* to the point of intersection. This line passes through point *P* and is perpendicular to *AB*.

1. Place compass point on the given point, and draw arc such that it intersects line twice.

2. Place compass on each arc intersection, and draw a further pair of arcs which intersect each other on the other side of line from original point.

3. Using a straight edge, connect this intersection to the original point with a straight line.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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