Edexcel IGCSE Maths 复习笔记 4.5.1 Loci & Construction

Edexcel IGCSE Maths 复习笔记 4.5.1 Loci & Construction

What are loci and constructions?

  • 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:

Perpendicular-Bisector

 

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:

 

Perpendicular-from-Point-to-Line 

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:

 

Angle-Bisector 

Exam Tip

Make sure you have all the equipment you need for your maths exams, along with a spare pen and pencil.  Rubber and pencil sharpener can be essential on these questions as they are all about accuracy.  Make sure you have compasses that aren’t loose and wobbly, make sure you can see and read the markings on your ruler and protractor.

Worked Example

7.17.1-Loci-Construction-Worked-Example-1General-Triangle-ABC7.17.1-Loci-Construction-Worked-Example-2

Worked Example

General-Triangle-ABC-with-arcs7.17.1-Loci-Construction-Worked-Example-3

Worked Example

General-Triangle-ABC-with-angle-bisected-shaded

Worked Example

7.17.1-Loci-Construction-Worked-Example-4Towns-and-Masts

Worked Example

7.17.1-Loci-Construction-Worked-Example-5Towns-and-Masts-with-arcs

Worked Example

7.17.1-Loci-Construction-Worked-Example-6Towns-and-Masts-with-arcs-bisector7.17.1-Loci-Construction-Worked-Example-7

Worked Example

Pair-of-Compasses-and-Ruler7.17.1-Loci-Construction-Worked-Example-8

Worked Example

Town-and-Masts-Complete7.17.1-Loci-Construction-Worked-Example-9

转载自savemyexam

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