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Loci and constructions - AQAConstructions between points and lines

Loci are a set of points with the same property. Loci can be used to accurately construct lines and shapes. Bearings are three figure angles measured clockwise from North.

Part of MathsGeometry 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

Constructions: bisecting lines and angles

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