Bearings and Loci in Geometry
This page covers the fundamental concepts of bearings and loci in geometry, providing essential information for students learning about spatial relationships and geometric constructions.
Compass Directions and Bearings
The document begins by introducing compass directions and their relation to bearings. How to use bearings in geometry is explained as an alternative method to describe locations.
Definition: A bearing is an angle measured clockwise from the North direction, expressed in three digits e.g.,035°.
Measuring Bearings
The page provides a step-by-step guide on how to do bearings in Maths:
- Draw a straight line between two points
- Draw a North line from the reference point
- Measure the angle between the North line and the straight line, moving clockwise
Example: Measuring the bearing of city A from city B results in 275°.
Complex Bearing Calculations
A more challenging example demonstrates how to use bearings in geometry when given partial information:
Example: Calculate the bearing of C from O when the bearing of O from C is 330°.
This example illustrates the use of angle facts about parallel lines and angles on a straight line to determine the unknown bearing.
Loci in Geometry
The concept of loci is introduced as sets of points meeting certain criteria.
Definition: A locus is a set of points that satisfy a specific geometric description.
Constructing Loci
The page concludes with instructions on how to construct an angle bisector with a compass and how to create a perpendicular bisector:
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For a perpendicular bisector:
Place the compass on one endpoint and draw arcs on both sides of the line
Repeat from the other endpoint
Connect the intersection points of the arcs
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For an angle bisector:
Draw an arc from the angle vertex, intersecting both sides
From these intersection points, draw arcs that cross each other
Connect the vertex to the crossing point of these arcs
These constructions are fundamental in understanding how to find the locus of two points and other geometric problems.
