# Constructions

## Perpendicular bisectors of a line

There are several constructions that you will need to be able to perform. Full explanations about how to perform them are on the videos here.

The perpendicular bisector of a line is a line that is at an exact right angle to another line.

Step 1: Set your compass to slightly more than half way over the line

Step 2: Place your compass on the edge of the line

Step 3: Draw arcs above and below the line

Step 4: Move the compass to the other end of the line and draw arcs again

Step 5: With a pencil and a ruler join the points where the arcs cross

## Constructing a perpendicular bisector

Step 1: Put your compass on the point ( P below) and create an arc that crosses the line.

Step 2: Move your compass onto the point where it has crossed the line then draw an arc

Step 3: Move your compass onto the point where the arc in Step 2 crosses the line and draw another arc

Step 4: Draw a line from the point P to the point where the arcs cross.

## Loci Problems

You can use these constructions to help you solve loci problems!

A common problem is to construct a loco around a line to do this you need to use a compass and a ruler.

Firstly, draw two secs around the ends of the line:

In this case we want a loci of 2 squares, so we make sure the compass is set to that amount.

We then complete the loci by drawing two straight lines, two squares away from the original line.

Now we have our loci!

## Perpendicular Distances

The perpendicular distance from a point to a line is the shortest distance to the line.

- What shape can you draw exactly to find angles of 60 degrees?
- Triangle