Loci and constructions – WJECConstructions between points and lines

To draw constructions you need a pencil, ruler and a pair of compasses. Loci are used to identify areas that satisfy criteria such as a given distance from a point or halfway between two lines.

Part ofMathsGeometry and Measure

Constructions between points and lines

Constructions are accurate diagrams drawn using a pair of compasses and a ruler.

When drawing constructions, the construction lines must not be rubbed out.

Constructing the perpendicular from a point to a line

Example

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P is a point above a horizontal line. Construct the perpendicular from point P to the line
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Open a pair of compasses so the distance is slightly longer than the distance from P to the line. Place the compass at point P and draw two arcs, crossing the line either side of P
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Put the compass point at E and draw an arc below the line. Repeat from point F without changing the width of your compass so the arcs cross to create point G
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Place a ruler between P and G. Use a ruler to connect point P to the line. The line is at a right angle to EF

Constructing the perpendicular from a point on a line

Example

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Q is a point on a line. Construct a perpendicular at Q
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Put the compass point at Q. Draw two arcs crossing the line either side of Q
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Put the compass point at S and draw an arc below the line. Repeat from point T without changing the width of your compass so the arcs cross to create point V
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Use a ruler to connect point Q to where the two arcs cross, at V. The line QV is at a right angle to ST

Bisecting an angle

Constructing circles

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