What are loci and constructions?

• A?locus?(loci?is plural) is a line/shape/path that is determined by following a rule – eg. always being 2m away from a wall
• You may be asked to?construct?a locus, although the language used in exam questions don’t always mention these words as questions are often based on real-world situations
• It is an excuse to get the maths toys out –?rulers?and?compasses?in particular!
• You will often be working with scale drawings with this topic

What do I need to know?

• There are some basic loci – like a circle for being a certain distance away from a point (eg distance a mobile phone mast can reach) and a straight line for being a certain distance away from another line
• These notes focus on three of the more complicated constructions and their uses:

1. Perpendicular bisector

• Maths:? A line that cuts another one exactly in half (bisect) but also crosses it at a right angle (perpendicular)
• Uses:? Shows a path that is?equidistant?(equal distance)?between two places, if you are on one side or the other of this line you know you are closer to one place than the other
• Final result:

2. Perpendicular to a line, from a point

• Maths:? This is drawing a line, perpendicular to another, but the line has to go through a particular point
• Uses:? Shows the?shortest?distance from the point to a line – eg. the shortest distance from a lighthouse to the coastline
• Final result:

3. Angle?bisector

• Maths:? A line that cuts an angle exactly in half (bisect), either side of the line shows you are closer to one line making the angle than the other
• Uses:? Shows a region on a map/diagram that is closer to one side than another
• Final result: