Drawing Lines at the Right Angle

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SUMMARY

The discussion focuses on techniques for accurately drawing lines at right angles using symmetry and mirror reflections. The user initially employed symmetry for the first two parts but struggled with precision in the third part. A suggested method involves utilizing the properties of plane mirrors, where the image of an object is directly opposite and equidistant from the mirror's surface. By drawing the image of point P inside mirror Y and then using that image as a reference for mirror X, one can achieve accurate angles.

PREREQUISITES
  • Understanding of basic geometric principles
  • Familiarity with the properties of plane mirrors
  • Knowledge of symmetry in geometric constructions
  • Ability to visualize reflections and angles
NEXT STEPS
  • Research techniques for constructing geometric figures using symmetry
  • Explore the principles of reflection in optics
  • Learn about geometric constructions with compass and straightedge
  • Investigate advanced methods for angle bisectors and perpendicular lines
USEFUL FOR

This discussion is beneficial for students of geometry, artists seeking precision in their drawings, and anyone interested in the practical applications of mirror reflections in design and construction.

david18
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For the first two parts of the question I simply used some symmetry to get the lines meeting the mirror at the correct angle. However for part c) whilst I know roughly what it should look like the angles aren't very accurate. Is there any simple method like the use of symmetry to draw lines at the right angle?
 
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Here's a trick that might help you. A plane mirror produces an image of an object that is directly opposite the object and the same distance inside the mirror. Using that, you can immediately draw the location of the image of P inside mirror Y. Then that image acts as an object as far as mirror X is concerned--draw that second image inside mirror X.

See if that helps.
 

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