Constructions and loci

Last time

Before we start: last time, in Bearings, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.

A goat on a rope

A goat is tied to a post by a rope five metres long. Where can it reach? Every point exactly five metres from the post, and everything inside. That set of points, following a rule, is called a locus. Today you build exact shapes with a ruler and compasses, and then draw loci.

Rules of the game

In a construction you may use only a ruler and a pair of compasses. A protractor gives no marks. Keep all the construction arcs. The examiner looks for them, and rubbing them out loses marks. Use a sharp pencil, and keep the compasses fixed once set.

Bisecting a line

Open the compasses to more than half the length of the line. Put the point on one end and draw an arc above and below. Without changing the width, repeat from the other end. The arcs cross in two places. Join the two crossing points with a ruler. This line cuts AB exactly in half, at a right angle.

Bisecting an angle

Put the compass point on the corner. Draw an arc crossing both arms of the angle. From each crossing, draw an arc of the same width inside the angle so the arcs meet. Join the corner to where the arcs meet. A sixty degree angle becomes two thirty-degree angles.