MathsNet: C - Construction - Equal distance from 2 lines

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Page ID: 10127

C | Construction | Loci | «Equal distance from 2 lines»

You will need to be able to use straight edge and a pair of compasses to carry out constructions. Below, the steps for a standard construction are described and an interactive illustration of the construction is shown.

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Summary/Background

A locus is a rule that describes where a point can be positioned on a graph or other diagram. A typical rule could be: all points 3cm from the point (2,5). This would be a circle. Or all points that are the same distance ("equidistant") from the points (1,3) and (5,4). This would be the straight line perpendicular to and bisecting the line between the points.

Software/Applets used on this page

JSXGraph

This page uses JSXGraph

JSXGraph is a cross-browser library for interactive geometry, function plotting, charting, and data visualization in a web browser. It is implemented completely in JavaScript, does not rely on any other library. It uses SVG and VML and is fully HTML5 compliant.

Glossary

circle

a conic curve with equation (x-a)²+(y-b)²=r²

edge

the line connecting two vertices of a graph, also known as arc or line.

function

A rule that connects one value in one set with one and only one value in another set.

graph

A diagram showing a relationship between two variables.
The diagram shows a vertical y axis and a horizontal x axis.

locus

A set of points that fit a given rule.

perpendicular

one line being at right angles to another.

rule

A method for connecting one value with another.

straight

The type of line produced by a linear equation.

Full Glossary List

This question appears in the following syllabi:

Syllabus	Module	Section	Topic	Exam Year
AQA GCSE (9-1) Foundation (UK)	G: Properties and Constructions	G2: Problem Solving with Ruler and Compass	Loci	-
CIE IGCSE (9-1) Maths (0626 UK)	3 Geometry	C3.8 Problem Solving with Loci	Loci	-
Edexcel GCSE (9-1) Foundation (UK)	G: Properties and Constructions	G2: Problem Solving with Ruler and Compass	Loci	-
GCSE Foundation (UK)	Geometry	Construction	Loci	-
OCR GCSE (9-1) Foundation (UK)	8: Basic Geometry	8.02d: Loci	Loci	-
Universal (all site questions)	C	Construction	Loci	-